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DATE DUE DATE DUE DATE DUE 11/00 chthfiS—p.“ SENSOR-LESS FLUX DETERMINATION IN INDUCTION MOTOR BASED UPON SATURATION EFFECTS USING HIGH-FREQUENCY MAGNETIZING CURRENT By Fida Muhammad Khan A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Electrical and Computer Engineering 1 999 ABSTRACT SENSOR-LESS FLUX DETERMINATION BASED UPON SATURATION EFFECTS USING HIGH FREQUENCY MAGNETIZING CURRENT By Fida Muhammad Khan As real-time computation costs continually decline, both mechanical robustness and economic considerations increasingly favor the replacement of mechanical sensors and transducers by software-based state estimation methods. The elimination of encoders or resolves on induction machine drives is a prime example. For high performance induction motor drives based on ”field- orientation’, it is necessary to determine the angle of a magnetic flux vector inside the induction machine (rotor, stator, air-gap) with respect to a stator frame. When this is done without a flux sensor and without a rotor speed/position sensor, the voltage/current, or v/i-model, is the means of determining this flux angle. The v/i- model has drift problems, especially at low flux frequencies. By analyzing the VA- model in the magnetic field coordinates instead of the fixed stator coordinates, the drift problem becomes a stability problem. Internal feedback methods still leave an operation area where such sensor-less control performance is low: the area around zero flux frequency [1]. In this frequency range the high frequency magnetizing current injection method can provide a way of determining the flux angle, even at zero flux frequency. This method is based upon saturation effects inside the induction machine and its structure is the basis of this proposal. Prior to this work, existing control methods by injecting high frequency estimation techniques for machines were design dependent [1 ,2-7]. Furthermore, the limitations of these existing and also newly emerging observer-based estimation techniques were not well understood nor well applied. This work first focuses on evaluating and improving the rotor flux estimation from stator voltage and currents for standard induction machines, without modification to rotor design. In this work, recent developments in the saturated model of induction machines and their use for obtaining the correct location of the rotor magnetic flux for the induction motor are considered. In particular, the motion of stator current vector is transformed to the motion of the rotor current vector through a transformation ratio obtained from the motor magnetic saturation and the motion of the rotor current vector information is extracted from the motor voltage equations [3]. The method is based upon an effect that appears in the region of magnetic saturation. The transfer properties are derived from the equations of current fed (current regulated) induction machines taking saturation into account. Simulation results are presented to show that the algorithm combined with the saturated effect has promising results and would be able to achieve the zero speed control of sensor less induction motor. Copyright by FIDA MUHAMMAD KHAN 1999 To My Parents ACKNOWLEDGMENTS I would like to express my thanks and gratitude to Professor Elias Strangas for being my principal advisor and for his encouragement, support and guidance. I would also like to thank Professor Hassan K. Khalil, Professor Robert Schlueter and Professor Jerry D. Schuur for their time and effort in being on my committee. A special words of thanks are directed to my lab colleagues: ,Bader Aloliwi, Zanardelli Wes, Ali Khurram, Andras Diaz, Shanelle Hogan and John Kelly who provided me with friendship, and fruitful discussions. Many thanks to Marilyn, Roxanne and Brian for their assistance in the Department office and Laboratory matters. Also, I wish to thank all other members of the Electrical Engineering Department for their support, be it scientific, technical or other. Finally, I owe a special thanks to my Parents, my wife Shahnaz Khan and my kids for their encouragement, support and patience. vi TABLE OF CONTENTS LIST OF TABLES ............................................................................................... IX LIST OF FIGURES ............................................................................................... X IJST OF ABBREVIATIONS ............................................................................... XII CHAPTER 1 ......................................................................................................... 1 INTRODUCTION .................................................................................................. 1 Problem Statement ................................................................................ 3 Overview of Chapters ............................................................................. 4 CHAPTER 2 ......................................................................................................... 6 CONTROL STRATEGIES OF THE INDUCTION MOTOR ................................... 6 Introduction ............................................................................................ 6 Main Techniques of Sensor-Less Control of Induction Motor. ................ 9 Estimators Using Back EMF .................................................................. 9 Estimation Using Spatial Phenomena .................................................. 11 Estimation Using Saturation Effects ..................................................... 14 CHAPTER 3 ....................................................................................................... 16 MATHEMATICAL MODEL OF INDUCTION MACHINE ..................................... 16 Introduction .......................................................................................... 1 6 Three Phase Voltage Model ................................................................. 18 Saturated Model ................................................................................... 24 Magnetic Saturation ............................................................................ 27 Spline Interpolation .............................................................................. 28 CHAPTER 4 ....................................................................................................... 3O FLUX ESTIMATION BASED ON SATURATION EFFECT ................................. 30 Introduction .......................................................................................... 3O Locus of Test Vector ............................................................................ 33 Using Rotor Currents to Correct For Rotor Flux Position ..................... 37 Estimating Test Rotor Current From The Stator Voltage ...................... 40 Limitations of The Method .................................................................... 45 CHAPTER 5 ....................................................................................................... 48 APPROXIMATED TEST SIGNAL VOLTAGE VECTOR ..................................... 48 Introduction .......................................................................................... 48 Choice of The Reference Frame .......................................................... 49 Approximated Test Signal Voltage Vector Using Flux Linkages ........... 51 Approximated Test Signal Voltage Vector Using Rotor Flux and Stator Currents ............................................................................................... 56 Approximated Test Signal Voltage Vector Using Voltage Model .......... 62 vii CHAPTER 6 ....................................................................................................... 6‘5 SATURATED MODEL PARAMETERS-SIMULATION ....................................... 65 lncrementing of Inductance in Saturated Model ................................... 66 Saturated Flux Model ........................................................................... 70 Flux Model Under Dynamic And Steady State Conditions ................... 73 Alignment of Saturated Model .............................................................. 74 Conclusion: .......................................................................................... 78 CHAPTER 7 ....................................................................................................... 79 SIMULATION AND SIMULATION RESULTS ..................................................... 79 Tracking The Displacement Angle (y) ................................................... 79 Limitation of The Proposed Method ..................................................... 83 Field Weakening .................................................................................. 90 CHAPTER 8 ....................................................................................................... 95 EXPERIMENTAL SET-UP .................................................................................. 95 Introduction .......................................................................................... 95 Experimental Current Control Hard ware Set-up .................................. 98 Hysteresis Current Control ................................................................. 103 Digital to Analog Conversion .............................................................. 106 CHAPTER 9 ..................................................................................................... 108 CONCLUSION ................................................................................................. 108 FURTHER RESEARCH ................................................................................... 111 APPENDIX A .................................................................................................... 1 1 5 A-1 FLOWCHART OF RT-LINUX WITH INTERRUPT ROUTINE .................. 115 A-2 INTERRUPT SERVICE ROUTINE ........................................................... 116 A-3 RT-LINUX INTERRUPT TIMINGS ........................................................... 117 APPENDIX B ................................................................................................... 1 18 8-1 RT-LINUX C-LANGUAGE PROGRAM FOR ON LINE SYSTEM ............. 118 B-2 OUTPUT DATA PROGRAME FOR ANALYSIS ....................................... 122 BIBLIOGRAPHY .............................................................................................. 127 viii LIST OF TABLES Vector Control Strategies of Induction Motor 8 Breakdown of time spent during one interrupt cycle using A/D converter 107 LIST OF FIGURES Figure 2.1 Vector diagram: Field orientation of the induction machine Figure 3.1 Schematic of the quadrature phase model (Natural reference frame) Figure 3.2 Schematic of the quadrature-phase model Figure 4.1 Model of the test current transfer function Figure 4.2 Saturation curve of the induction motor Figure 4.3 Locus of the stator current test vector Figure 4.4 Locus of the induced rotor test current Figure 4.5 Construction of the stator current test vector. Figure 4.6. Real flux is in line with the estimated rotor flux Figure 4.7 Real flux is not in line with the estimated rotor flux Figure 4.8 Real flux and estimated flux are in line Figure 4.9 Block diagram of Real-Implementation Method. Figure 4.10 Construction of f3' when parts 1) and 2) are available Figure 4.11 construction of f‘3 when parts 1) and 4) are available Figure 4.12 Construction of 93’ when 1) and 4) are available Figure 4.13 Saturated condition due to small estimated Figure 4.14 Loss of saturation due to large estimated flux Figure 5.1 Different coordinates axes in AC machine modeling Figure 6.1 Magnetization curve Figure 6.2 Field-Oriented Saturated Induction Motor current-fed Model Figure 6.3 Induction machine flux linkages space phasors Figure 6.4 Vector components under field orientation Figure 6.5 Fundamental Component current and flux vectors in the rotor flux field oriented under steady state loaded condition Figure 7.1 Simulation model for saturated Motor Figure 7.2 The Error Angle Vs the angle between actual and estimated flux Figure 7.3 Using the angle yto correct for rotor flux estimation Figure 7.4 Saturated condition due to small estimated Figure 7.5 Loss of saturation due to large estimated flux Figure 7.6 Effects of large angle error and increased test frequency on the shift angle, 7. Figure 7.7 Variation in magnetizing parameters Figure 7.8 Transition from DFO to Estimated Error method Figure 7.9 Switch from saturated model to DFO -simu-link block Figure 8.1 Experimental setup Figure 8.2 Hardware and software schematic of the experimental set up Figure 8.3 Signal flow in the experimental setup Figure 8.4 Hysteresis current control: (a) signal flow diagram; (b) basic current waveform Flowchart of RT-Linux Based System with interrupt routine Interrupt service routine xi Subscripts Superscript Quantities isAvistisC LIST OF ABBREVIATIONS Stator rotor three phase system stator reference frame rotor flux reference frame rotor reference frame Leakage magnetizing general reference estimated command stator three phase currents, rotor three phase currents stator currents in the stator reference frame (RF) rotor currents in the stator (RF) stator currents in the rotor (RF) rotor currents in the stator (RF) test stator current vector tBSt rotor current VBCtOI‘ component of the test rotor current (A;r ), in the rotor flux-RF component of the test stator current (AIS ). in the rotor flux-RF stator test current vector in the test current coordinates. xii K1 ,K2 _ ‘er L‘ 41an -121 'Fran t"| a La! UsA,UsB,UsC, UrA,Ure,Urc, Vso,Vro Vsa'VSb Vfa'Vrfi rotor magnetization current test current transfer factors tangent or dynamic (tangent-slope or incremental) inductance static (chord slope or amplitude) or chord inductance magnetizing inductance stator leakage inductance rotor leakage inductance stator self-inductance of one stator phase winding total three-phase stator inductance total three-phase rotor inductance rotor self-inductance of one stator phase winding resultant three phase magnetizing inductance mutual inductance between two stator windings mutual inductance between two rotor windings maximum mutual inductance between the stator and rotor are the effective number of rotor and stator turns refrence frame stator and rotor resistance of phase windings motor slip modified rotor time constant including saturation effect rotor time constant stator instantaneous three phase voltages rotor instantaneous three phase voltages stator, rotor zero-sequence component stator voltages in an equivalent two-phase stator winding rotor voltages in an equivalent two-phase rotor winding xiii V,(ab) riflab) rotor voltages and currents in the stator reference frame W94“) stator and rotor space phasor flux linkages W94”) stator and rotor space phasor flux linkages \Vr actual rotor flux lit, estimated rotor flux 8, the rotor angle to, stator flux speed called synchronous speed (09 speed of general reference frame a), rotor speed ms," rotor flux speed p estimated rotor flux angle p actual rotor flux angle [3 angle of the tangent in the operating point 6 angle with respect to the origin of the curve angle difference between the rotor test current vector and the stator test current vector test angle in the estimated flux of reference. difference angle between the estimated and the actual flux. Mathematical symbols =_d_ dt Miscellaneous DFO Direct Filed orientation IDFO Indirect Filed orientation HPF High Pass Filter LPF Low Pass Filter RT Real Time xiv Chapter 1 INTRODUCTION Induction motors constitute a theoretically interesting and practically important class of nonlinear systems, which are evolving into a benchmark example for nonlinear control. They are described by a fifth order nonlinear differential equation with two inputs and only three states available for measurement. Control objectives are complicated by the fact that the operation of induction motors is subject to unknown (load) disturbances and the parameters are highly uncertain and subject to variation. The machines/control engineers are faced with the challenging problem of controlling a highly nonlinear system, with time varying parameters, where the regulated outputs, besides being not measurable, are perturbed by unknown additive signals. Existing solutions to this problem, in particular the de-facto industry standard field- oriented control, suffer from some drawbacks, both in commissioning and in high performance applications [4]. These factors, together with recent developments of powerful theoretical tools for analysis and synthesis of nonlinear systems, have compelled machine/control researchers to tackle this problem. Moreover, due to decline in the computational cost at real time, nowadays field orientation of the three-phase ac induction machine is carried out without using flux sensors, but only using easily measurable stator voltages and stator currents. High performance induction machine drives in use today exist as the result of the simultaneous development of the two key technologies: electronics including both power electronics and microelectronics, and machine/drives control theory. Implicit within these two are sensor and state estimation technologies. Induction machine design has played a lessor role. Beyond becoming more efficient and compact, the induction machine has not changed substantially over the last half century. The theory of space vectors developed in the late 50’s is credited with providing the necessary foundation for the analysis of AC machine dynamics. New control methods based upon moving frames of reference aligned with flux vectors were introduced in the early 70’s. These methods greatly simplified the analysis of AC machines dynamics by enabling the de-coupling of the flux and armature axes inherent in DC machines. Field orientation did not gain wide industrial acceptance until the advent of digital implementation means, especially microprocessor and Digital Signal Processor (DSP), in 80’s. By enabling the implementation of complex control functions in the software, the hardware requirements are becoming more economical. Self-tuning and online adaptation of the plant and mechanical sensors [5,6] and internal sensors for measuring flux are generally regarded as unacceptable for all but very low power systems. The inherent flexibility of software implementation enabled control schemes to be extended and improved upon as DSP computational power increased. Thus direct and indirect field oriented flux techniques based upon machine models have evolved. The limited accuracy of existing estimation techniques and the requirement of rotor position/velocity feedback for torque control at zero and low speeds have been two significant factors forestalling the complete replacement of DC drives. The functional integration of machine design with state estimation, control and drive technologies has the potential of overcoming these limitations [4,7]. But the motor design changes requires additional process stages during manufacturing and will add cost and inventory burden to a low margin production. 1.1 PROBLEM STATEMENT 1. The major contributions of this work include the development of the saturated induction machine theory in order to use it to sense the position of the rotor flux. This scheme is in relation to the demand of a high performance at very low frequencies. In particular, the following are presented here for the saturated motor: 1.1 Analyze the relationship between the stator and rotor currents and fluxes. 1.2 Simplify the relationships described in 1.1 above, and develop a similarity and simplified relationship for the stator voltages that can be implemented in a controller. 2. Find the limits of the proposed method in terms of initial errors in the estimation of flux the position, effects of test and power frequency etc. 3. Develop a smooth way to transition between low-speed operation using of saturated induction motor with injection of high frequency magnetizing test current and higher speed operation with direct field orientation (DFO). 1.2 OVERVIEW OF CHAPTERS Chapter 1 provides a literature review of the main techniques of sensor- less control of induction motor for high-performance applications including state estimation and control Strategies of the Induction Motor. Chapter 2 outlines the main techniques of sensor-less control of the induction Motor for high-performance applications, including state estimation and control Strategies. Open-loop and closed-loop rotor flux observers are evaluated with particular emphasis on estimation accuracy. Further, the limitations of the transducer-less direct field orientation (DFO) and the indirect field orientation (IDFO) are investigated using voltage and flux models. An improved system is proposed Chapter 3 gives the derivation of the unsaturated induction motor model and then derives the saturated induction model. There a method is developed for calculating the inductance parameter from the motor magnetization curve. Chapter 4 and Chapter 5 are experimental verifications. The improvements are incremental and very optimistic, however, they do not overcome certain fundamental limitations. To overcome the limitations, more active to flux estimation at zero frequency is developed in Chapter 4 and Chapter 5 without integration. A new closed system is presented based upon the injected high frequency technique. These chapters also focus on the different derivation of saturated induction motor voltage equations used for simulation. These equations and their derivations are based on the saturated effect. Chapter 6 presents the behavior of induction motor parameters in saturated conditions under dynamic and steady state conditions. Rotor flux direct field orientation (DFO) approaches based upon the new methods are analyzed and developed chapter 7 to be used in conjunction with the proposed technique for high speed operation. Chapter 9 describes the experimental setup and the use of Real Time Linux(RT-Lunix) for this thesis. Chapter 9 ends with conclusion and further research to be carried out on this thesis. Chapter 2 CONTROL STRATEGIES OF THE INDUCTION MOTOR 2.1 INTRODUCTION The present state of the art in the field-oriented (or vector control) technique was introduced by Blaschke [8]. This method consists of rewriting the dynamic equations of the induction motor in a reference frame that rotates synchronously with the magnetic flux inside the machine. This can be the stator flux, the rotor flux or the air gap fluxes, figure 2.1. stator 'sa Fugure 2.1 Vector diagram: Field orientation of the induction machine In the rotor field coordinate system, one observes that by holding the rotor flux constant using one input (ix) , there is a linear relationship between the second input, (iy) and the torque. For the other two coordinate systems, the relationships are also relatively simple. For field orientation, the flux vector in the induction machine, especially its angle, has to be known. This flux angle can be found in the three different ways: a). By a measuring the magnetic field inside the machine with Hall sensors or sense coils. These sensors are mechanically vulnerable and costly to install. b) By using a machine model, the so-called current model, fed by the stator current and the rotor speed or angle model. This requires a shaft encoder that is often undesired, because it is an extra mechanical component with separate wiring. o) By using a machine model that needs only the stator voltage and current as its inputs. This is the voltage/current model and enables a sensor-less field-oriented control, because no additional flux or speed/position sensors are necessary. The sensor-less field-oriented control by means of the voltage/current model is the preferred way of highly dynamic induction machine control, and is the basis of this proposal. Field orientation enables a simple decoupling control similar to DC machine control and serves three purposes: i) to maintain a constant flux level; ii) to limit the current; iii) to stabilize the ac machine. Electric and hybrid electric vehicles and industrial speed controlled drives are usually controlled by the preferred method of indirect vector control. However, this method requires a speed encoder on the machine shaft and feed-fonNard slip frequency signals for the generation of the vectors. The encoder provides the speed feedback signals, which are used in the generation of the unit vectors and for speed control. Typically, the speed encoder is undesirable because it is expensive, fragile and requires an additional wire harness and connectors which can be unreliable in the drive system. The direct vector method generates the flux vector from the machine terminal voltages and currents, without the need of a speed encoder. Relating to the process of calculating the flux space phasor position, 0, the direct and indirect methods use estimators for the stator voltages, currents and speed measured, and known motor parameters. At low speeds (and low frequencies) direct methods are susceptible to noise, and DC offset and are better suited for high speed applications. Indirect methods based on current models are sensitive to changes in the rotor time constant, and othenlvise are appropriate at low speeds. Boldea and Nasar [9] summarize the most appropriate strategies for the vector control of induction motors in table 2.1. Table 2.1 Vector Control Strategies of Induction Motor Flux Current Voltage Combined Indirect Direct Orientation Control Control Voltage Method Method and Current Rotor Flux Most Most Most Orientation Appropriate Feasible Appropriate Appropriate Feasible Stator Flux Most Most Orientation Feasible Appropnate Feasible Feasible Appropnate Airgap Flux Most Most Orientation Appropnate Feasible Feasible Feasible Appropnate 2.2 MAIN TECHNIQUES OF SENSOR-LESS CONTROL OF INDUCTION MOTOR. Since the end of 1980s the estimation of the rotor position, or the position of the rotor flux, has been the subject of intensive research. The methods utilized include a variety of control theory approaches, and the state of the art is detailed in [10—11,1]. Estimators using intelligence (neural networks, fuzzy-Iogic-based systems, fuzzy-neural networks and genetic algorithms) have also shown some promising results. Various techniques used in high performance drives for the estimation of the slip, rotor, speed, rotor angle, and various flux linkages are discussed in section 2.3. Most methods of transducer-less velocity estimation of the induction motor utilize the back emf based upon the fundamental component model of the machine. To evaluate such approaches, two basic facts should be recognized; 1) Rotor flux is not fixed in magnitude or position relative to the rotor, thus, velocity estimation via back emf is more difficult and parameter sensitive in induction machines than in DC or synchronous machines and 2) Spatial dependencies are not intrinsically within the fundamental design of symmetrical induction machines, so that when needed artificial saliencies must be introduced. 2.3 ESTIMATORS USING BACK EMF 2.3.1 Open-loop estimator using monitored stator voltages/currents In open loop estimators, especially at low speeds, parameter deviations have significant influence on the performance of the drive both in the steady state and transient state. The stator resistance (Rs) has important effects on the stator flux linkages, especially at low speeds. In some schemes, the rotor flux-linkage estimation requires the knowledge of the rotor time constant (T ng/R.) The rotor resistance can vary due to temperature and skin effects, and Lm can vary due to skin and saturation effects. The thermal model of the induction machine or adaptive control and self commissioning schemes are used to minimize the effect of parameter deviation[10,12 ,13, 14]. 2.3.2 Model reference adaptive systems (MRAS) As stated above, the open loop estimators strongly depend on the machine parameters. In MRAS system some state variables, e.g. rotor flux and the back e.m.f are estimated from the stator voltage and currents in the estimated model and then are compared with the state variables estimated by using an adaptive model [10,14,1, 15, 16]. The difference between these state variables is then used in an adaptation mechanism, which outputs the estimated value of the rotor speed and adjusts the adaptive model until satisfactory performance is obtained. Using Popov’s criterion of hyperstability the adaptation mechanism is derived. The MRAS technique can be robust with respect to the stator and rotor resistance, which can be used at low speeds, e.g. 0.3Hz, [8]. Problems arise at extremely low frequencies, due to incorrect flux estimation. 2.3.3 Observer (General, Kalman, Luenberger) A closed-loop estimator is referred to as an observer. It is possible to improve the robustness against parameter mismatch and also additive noise by using closed loop observers. The Kalman filter (KF) observer is of the stochastic 10 type and Luenberger observer (L0) is of the deterministic type[6,16]. Both types the KF and LO can be applied to linear and non-linear systems. Various industrial a.c. drives already incorporate observers [17]. However, when the stator frequency is very low, its non-linear observability becomes weak for both flux linkage and speed estimation and it can not operate at zero speed. Accuracy Limitations: the entire above estimator algorithms used for sensor-less operation fail to operate at zero stator frequency region [5]. At zero no signal frequency is available from which rotor dynamics can be measured. Performance of sensor-less drives is inferior to that of the sensor-based drives at low frequency. For applications where very low-speed operation is less important than the high speed, direct field orientation gives satisfactory torque control performance. 2.4 ESTIMATION USING SPATIAL PHENOMENA An example of velocity estimation based upon spatial phenomena inherent within the machine is using the tracking of induced voltage or current ripple due to rotor slotting. Viable estimation has been demonstrated under steady state, medium-high speed, medium-high speed load operating conditions, but not at low and zero speeds and/or light loads [4 5 7]. Other forms of potentially useful phenomena occurring within the induction machine include rotor/stator eccentricities and winding/cage asymmetries. Because such phenomena relate directly to rotor position, tracking of spatial phenomena offers higher potential in terms of position and velocity estimation accuracy than the 11 back-emf-based approaches. Unfortunately intrinsic spatial phenomena are often inadequate for robust tracking. Furthermore existing approaches lack the capabilities of dynamic estimation of position, or even velocity. Real-time fast Fourier transformation were utilized by Ferrah, [18] to identify the speed-dependent slot ripple harmonics in the measured stator currents. A search scheme based upon a peak-picking algorithm was used to isolate the slot harmonic. Successful operation was claimed under different load levels and velocities. The amplitude of the rotor slot harmonics were shown to vary with load. However, under light loading, the amplitude of third harmonics was insufficient for tracking. Hurst [19] proposed a velocity estimation scheme based upon the isolation of a particular rotor slot harmonic in the stator currents, followed by pulse counting to obtain velocity. Although measured current spectra are provided, experimental verification of velocity estimation is not provided, this approach lacks the capability of tracking the flux at zero speed Another group of sensor-less algorithms uses the non-ideal machine characteristics such as eccentricity of rotor, rotor slots harmonics, and rotor unbalance. These algorithms requires frequency spectrum analysis, and they are time consuming and need some machine construction data such as number of rotor slots and stator slots, which can not be easily obtained for off-the-shelf motor. Rather than tracking slot harmonics in the stator currents, in a much earlier approach lshida and Iwata [20] tracked slot harmonics in the stator voltage. The three phase voltages were summed to isolate harmonics. By 12 sampling the assumed voltage at a multiple of the excitation frequency, a signal with a multiple of the slip frequency was obtained. A zero crossing detector generated pulses of constant area that were smoothed through a low-pass filter to obtain the estimated slip frequency. Good results were claimed in the speed range of -50% to +30% of the stator frequency, but the method has limitations especially under dynamic conditions or low speeds. Even with the modern digital signal processing algorithms, still the performance of the speed control bandwidth of the drive appears like unsatisfactory. Zinger, Lipo, and Novotny [21] implemented a field oriented drive that utilized the voltage measured across tapped stator windings for flux and rotor speed sensing. The speed was estimated by detecting the rotor slot ripple voltage harmonic. To isolate the slot ripple, the voltages of three coils displaced by 120° were summed, leaving primarily a 3rd harmonic due to saturation and a slot ripple. A switched-capacitor band-pass filter with a center frequency that tracked the slot ripple provided further isolation. A phase locked loop was used to track the slot ripple frequency and yield rotor speed. The steady state performance was good at high speeds, but at low speeds, below 5H2, the slot harmonic signal became too small to track. Cuzner, Lorenz and Novotny [22] demonstrated the principle and operation of velocity and position control sensing approach for an induction machine using the motor terminal properties and torque command (assuming Field Orientation) [23]. A closed loop non-linear observer was proposed to calculate (in real time) the rotor position and speed based upon an analytical 13 model of the machine magnetic saliencies and winding asymmetries. The observer calculates the harmonic spatial components in the emf. After comparing then to the measured emf they are used to drive the observer to accurate position and speed estimates. An important conclusion was reached, that machine designers should consider intentionally incorporating magnetic saliencies and winding asymmetries into future machines. This method can not be reliably applied to the existing standard induction machines. Another category of algorithms is the heterodyne method that requires injecting a signal to the motor terminals and checking the response of the motor to this injected signal [7]. This algorithm gives reasonably satisfactory performance for the induction motor with open slot rotor. But in the case of closed rotor slots, as is the case with most of small and medium power squirrel cage induction machines, this algorithm does not work well, especially at loaded conditions. This is because of saturation effects on the leakage inductance with load current flowing in the rotor circuit. The torque controllability in the low and zero frequency region is not adequate for off-the-shelf general purpose inverter fed conventional squirrel cage induction motors. So far, most algorithms do not work well with the mass-produced closed rotor slot motor in the zero or low stator frequency region under heavily loaded conditions. 2.5 ESTIMATION USING SATURATION EFFECTS The flux estimation schemes in the previous sections were not based upon the fundamental induction machine equations. Alternative approaches were 14 developed based upon secondary effects such as saturation. An obvious limitation of saturation-based approaches is their incapacity of field-weakened operation. Operation of a machine in a saturated state creates a third harmonic spatial component in the air gap flux and phase voltages. Kreindler [24] developed and demonstrated a direct field oriented controller using third harmonic component. By summing the phase voltages of the wye-connected machine, the third harmonic was isolated, in addition to rotor slot ripple components. Since the third harmonic is fixed relative to the air gap flux, the relative flux angle could be directly determined. The rotor flux angle is obtained upon compensation for rotor leakage inductance, position feedback is not required. Furthermore, the low speed limitations of the voltage model involving integration and sensitivity to stator resistance are absent. However, because the third harmonic amplitude is speed dependent, the method still fails at zero and low speeds. 15 Chapter 3 MATHEMATICAL MODEL OF INDUCTION MACHINE 3.1 INTRODUCTION For the purpose of understanding and designing vector controlled drives, it is necessary to know the dynamic model of the induction machine. Such a model, valid for any instantaneous value of voltage and current, and adequately describing the performance of the machine under both steady state and transient operation, can be obtained by utilizing the space phasor theory. In the stationary reference frame the stator voltage equation can be expressed as: _ _ di—Ils _ - (A30 (3.11 US(ABQ — RS °IS(ABQ + ——_dt — T dWflABC) (3'2) Ur(ABC) = Rr-1r(ABC) 1' T A similar expression holds for the rotor voltage equations expressed in the reference frame fixed to the rotor: Where the UsA,UsB,UsC, and U,A,U,B.U,C, are the stator and rotor instantaneous phase voltages; similarly is,(,i,,B,isC and i,,,,i,,,,i,C are the stator and rotor three phase currents, Rs and Rr are the resistance of stator and rotor 16 phase windings. The instantaneous values of the stator and rotor flux linkages components, can be expressed as: vsA = LslsB + MslsB + MslsC + Msr coserer VsB = EsisB + fisisA + fisisC + MS, cos(9r + 41t/3)irA + Msr cos 991-13 + fisr cos(6r + 2"/3)irC + Msr cos(6r + 21t/3)1rB + Msr cos(6r + tin/3):rC VsC = EsisC + fisisB + fisisA + fisr cos(9r + 21t/3)irA + fisr cos(9r + 41r/3)irB + M-sr cos erirC VrA = ErirA + I‘d-rid; + firirC + Elf—S, cos GrisA + Ms, cos(9r + 41t/3)iSB + 175,. cos(0r + 21c/3)isc m = trim + firim {mire +315, cos(9r + 2n/3)i5A +MS, cosOrisB +118, mm, + 4“/3)isc VrC = ErirC + firirA + Erin-B + M81. cos(6r + 41t/3)isA + Msr cos(9r + 21t/3)isB + Msr cos Grisc where 8, is the rotor angle i.e between the rotor axis and the stationary axis. The stator self-inductance of one stator phase winding is can be expressed as the sum of the stator leakage inductance L3. and the stator magnetizing inductance Lsm, (Es: Ls. +Lsm,), whereLsm =(N,/NS)MS,, N, and Ns.are the effective number of rotor and stator turns. The mutual inductance between two stator windings Ms = Lsrn COS(21c/3) = — L3,, . Similarly, the rotor self- inductance E: L,. +er, whereLmu =(N,/Ns)Msr, and the mutual inductance between two rotor windings M, =er COS(2n/3)=-l—-2"l. The maximum value of mutual inductance between the stator and rotor, M5, = Lserm . The resultant three phase magnetizing inductance can be written as Lm= 3M5“ then it follows 2 from above that the total three-phase stator inductance Ls takes the form 17 LS =IS —Ms 2 L31 +Lsm +-;-Lsm = Ls] +§Lsm, Similarly, the total three-phase rotor inductance L, takes the form L, = E, — M, = L,l + L,m + iL,m = L,, + 3L,m 2 2 3.2 THREE PHASE VOLTAGE MODEL Substituting, the above instantaneous values of the stator and rotor phase-variable flux linkages components into equations (3.1) and (3.2) of the three-phase machine can be combined into single matrix equation. 'usA] _ RsiPLs PM;_ PM PM,cos9 PM,cosB1 PMrcosez [isA1 UsB PL’E 3.,in PM; PMsrcosez Pit/90°89 PM,,COSB1 isB Usc _ _P'V!e. P'VE Rs+PLs PMsrCOSBI P'VErgOSfb PMsr_0099 isc U,A PE,cos9 PM,cos92 PM,cose, R,+_PE, PM PM 'irA UrB PMs,cos8, PIl—flsrCOSB PMg,cosez PM R,+PEr PM irB _Urc_ [PIT/grcosez PM,mos81 PM5,cos8 PM PM R,+PL, J Lirc_ (3.3) Where P=j — ,which operates also on the inductances, since in general they can vary with current. The angle 0, is the rotor angle, between the rotor axis and the stationary axis; angles 6, 81 and 92 are defined as 9:0,, 01:9,4-21c/3,and 92:9,4-41t/ 3. 3.2.1 Transformation From Three Phase to Two Phase Model The above matrix is the impedance matrix of the three-phase model, which contains 36 non-zero elements. It is possible to achieve reduction in the elements in a balanced three-phase induction motor, which can be described as 18 an equivalent two-phase machine with a simpler mathematical model, containing 12 elements. Considering the equation 3.3 and using a transformation equation: Vo 2|:111111] U(s. r)A Vam) = " 2 ‘ U(s, r)B 6 Vb(|3) O J— _ -‘/— U(s, r)C Both stator and rotor equations can be transformed to 2-axis, 12 elements, simple voltage model. The zero-sequence component, V3,, and V,o in the above equations are zero, provided the power invertor do not contain a dc offsets. Due to symmetrical sinusoidal winding in the induction machine, it is assumed that there is no zero-sequence voltages and currents in the stator and rotor windings. The components V3,, and Vsb are the stator voltages in an equivalent two-phase stator winding that establishes the same result as the three-phase rotor winding. Similarly V,,, and V,B are the rotor voltages in an equivalent two-phase rotor winding. The same transformation technique can be applied for current transformation, for more detail refer to [25,8]. This corresponds to using a quadrature-phase machine model instead of the three-phase model. The transformation equation results in the two-phase voltage equations of induction motor in the natural reference frames: 3.2.2 Natural Reference Frame-Voltage Model (Unsaturated Model) Vsa ' R5 + FLs O FL,n cos 9, - FLm sin 9; isa Vsb = 0 R5 + FLs FL,“ sin 8, FL,n cos 9, isb (3 4) V“, FL“, cos 9, PLm sin 8, R, + FL, 0 , ira ' LVTB. L— PLm sin 8, FLm cos 9, 0 R: 1' FL, _ _iri3_ 19 Se Figure 3.1 Schematic of the quadrature-phase model (Natural reference frame) The equation (3.4) can be put into the following space-phasor form dWSGIb) dt Vs(ab) = Rsjs(ab) + d-‘I7r(or[3) VI'UXB) = O = RPM-((43) '1' dt The stator and rotor space phasor flux linkages are given by Wm» =Lsis(ab) +Lmi,(ab) and Wm,» =Lsi,(aB) +Lmis(a[3) where isa and isB are the stator currents in the rotor reference frame, and, i,a ,i,b are the rotor currents in the stator reference frame, (the transformation matrix are explained below). It follows from the equation (3.4) that as a consequence of the phase transformation, the machine model contains only 12 elements. The stator and rotor variables are in their natural reference frame, figure 3.2; and even if the machine parameters are constant, the system of voltage differential equations is time dependent, since the equations contain the rotor angle 0,, which changes with the time. If the inductances are independent of im, (unsaturated condition), the differential operator can be moved after the inductance element. However, by 20 transforming the rotor voltages and currents from the rotor reference frame to the stator reference frame, it is possible to achieve further reduction in the elements of the impedance matrix, i.e. eliminating the angles. The rotor current and flux linkages in the stator reference frame are related to the rotor current and flux linkages in the rotor reference frame by the following transformation: ir(ab) amuse“ =0... “Meier in, _ cos 9, —sin 8, im irb - sin 6, cos 9, L13 Similarly the rotor flux linkages can be expressed in the stator reference frame as: anb) : Mme“ = (Wm 'HI’rp) eje, Wm _ COS 61’ —Sin 91' Wm ‘l’rb _ sin 6, cos 6, \llrg Thus by considering the transformation equations, the transformed set of stator and rotor voltages can be expressed in the frame of reference fixed to the stator: 21 3.2.3 Stator Reference Frame-Voltage Model (Unsaturated Model) vs, R, + FLS 0 mm o is, Vsb _ 0 Rs '1' FLS 0 FL,“ isb Vra H“In (0er Rt + FLr (Dr-L1" ira Vrb — (0er FLm “' (0,1,, RI‘ + FLr ir'b (35) $th 'b E (:3 Figure 3.2 Schematic of the quadrature-phase model The above equation can be put into the following space-phasor form dvsmb) dt (3.6) VS(8b) = R5°is(ab) 'I" dMuab) dt (3.7) Vr(ab) = O = Rl'il’(ab) '1" Hence, the stationary-axis stator quantities are unchanged, but the rotor voltage and currents are transformed. The schematic of this machine is shown in figure 3.2; on the stator there are direct and quadrature-axis windings denoted by $3, sh and on the rotor there are windings denoted by re, n, respectively. V,(ab) and friab) are the rotor voltages and currents in the stator reference frame. Moreover, in the direct-axis rotor windings, the term P(Lm.isa +L,i,a) describes induces voltages by transformer effects, and (Ml-mist: +L,i,b) produces voltages due to the rotation. Under unsaturated magnetic condition, the differential 22 operator can be moved after the inductance, and when the motor is saturated, the differential operator can be moved before the inductance; this is discussed in the next section. However, instead of a reference frame fixed to the stator or rotor, a general reference frame is used, with direct and quadrature axes x,y, rotating at a general instantaneous speed mg=d09Idt, where 09 is the angle between the direct-axes of the stationary reference frame sa fixed to the stator and the real axis(x) of the general reference frame, hence the equations (3.6) and (3.7) can be written: d __ WSW) + 3'0)ng VsmrlLsIs(dq) +LmIr(dq)) (3-9) Vsrdq) = Rs-lsrdq) + 24 Vr(dq) = LmFmrl + K009 - (Dr )'\l7r(qd) 7 (N d 0 = Rr-'r(dq) + r( Q) where, im, is the rotor magnetization current: Later it will be shown that im, is a function of L... 0 = R,.i,(dq, + Lm 4:220] + mer " “ill-m Rmril (dLmjmlizqu dl—rl dilmrl 91ml dt chm] dt Lat— Fmrl ‘ is‘ldq) = (Fmrl — Ismq) )Lm where, 7 = HdQ) 1 + o, Lr lkrnol “isms + dmmlkml) + xwmr " mr)Lm|i(mr)| 0 = R,L,,, L, dt T,(——)—— L4 2:1 +| I—m] _ isdq — j(w,,,, —w,)T,|i,,,,l (3.10) T, = Tr(—>=L(—1*L‘t:RLr——m- ) =_r LrI'I'I-‘m (R )=(—— Rr ——-—-—) 25 where, L is a dynamic (tangent-slope or incremental) inductance, and it is equal to the derivative of the modulus of the rotor magnetization-flux space phasor with respect to the modulus of the rotor magnetization current space It should be noted that in contrast to this, L,,,=—— I—‘I is the static F mrl Fmrl (chord slope) or amplitude inductance. Moreover, T, is the rotor time constant, phasor, L- =—— which because of saturation is not constant. in this expression, L,. is the leakage inductance of the rotor, which has been assumed to be constant. Under linear magnetic condition L=L,,,. It must be mentioned that because of saturation, the modified time constant T,*, has chord and tangent inductance effects as a result of saturation. Hence, it is important to note that because of saturation, both T,* and T, are varying parameters and depend on the magnetization inductance, which changes with limi. When equation (3.10) is resolved into its real-(x) and imaginary-(y) components, the direct-axis flux model equation of the saturated induction machine in the rotor -oriented reference frame is obtained. qi—l l (3.11) Tr dt —+|i,,,,|=i,,, Wmr = WT+——- (3.12) “Fl 26 The equations (311,312) are in the rotor flux reference frame, involving only rotor voltage equations. Similarly, the saturated voltage model, in the stator reference frame can be derived form equation (3.8) and is expressed as following: Vsa RS + LsaP Lsap Lmap LabP Isa V8b __ LabP RS +stP LabP LmbP isb v“ LmaP 0)er + LabP R, +me erm +Lab its (313) V“, —(I),.L,m + LabP LmbP -—a),L,,, +L,,,P R, +L,qP id, 3.4 MAGNETIC SATURATION It is well known that, as the flux in the machine increases, the iron paths begin to saturate. Saturation prevents the machine from reaching the torque levels predicted by the linear magnetic model. Hence, it is desired to have a dynamic model of the induction motor, which includes saturation, in order for the controller to accommodate such effects. However, the modeling of saturation is by no means obvious and is still an active area of research. Recent progress in this area has been reported [6,23,26,27]. In a unique approach to modeling saturation, the 1: -model of the magnetic circuit is used rather than the standard T-model [23]. However, the determination of the saturation curves for this model requires the measurement of the rotor currents, which is not possible on the squirrel cage induction machine. In [26] saturation is modeled using air gap length that varies as a function of both position and level of the air gap flux, and 27 by the addition of some fictitious winding to generate third harmonic components. Experimental results are given showing the model predicts spatial saturation effects with good accuracy. However, this model is somewhat complex; this complexity in turn also makes the resulting nonlinear input-output linearization controller complex. In [8] Vas developed a model for magnetic saturation by making the mutual inductance a function of rotor magnetization current. The resulting model is complex but more practical and is used for this thesis. For constant speed applications, the flux is typically set to a constant value. For demanding speed trajectories, the flux reference must vary with the time. In particular, as the speed of the motor increases, the flux must be decreased (field-weakening). This is done because the inverter has current and voltage limit constraints. The standard method employed for field weakening is to decrease the flux as 1/0) after some base speed is reached. However, it is not clear how to choose this speed, nor is it clear that this is the best possible method to accomplish field-weakening, moreover, the 1/(0 scaling does not include saturation effects. 3.5 SPLINE INTERPOLATION For simulation process, the magnetization saturation curve for the induction motor is obtained from the unsaturated model by using a spline interpolation. The spline interpolation is a piece-wise polynomial interpolation. This means that if a function f(x) is given on an interval as x Sb. An approximate f(x) on this interval by a function g(x) that is obtained as follows: We 28 partition a Sbe;that is, we divide it into intervals with common endpoints, x0....x,,, called nodes, a= xo stator Figure 4.8 Real flux and estimated flux are in line In summary, the angle difference 8 between the estimated rotor flux vector and the actual rotor flux can be determined by measuring the angle 7 between the stator test current vector (which is in parallel with estimated rotor flux vector) and the induced rotor test current vector. 39 4.4 ESTIMATING TEST ROTOR CURRENT FROM THE STATOR VOLTAGE The induced test rotor current, described in the previous section can not be directly used for the flux determination, because the vector of the rotor current can not be measured. Normally this measurement cannot take place without modification of the machine. There is however a possibility to obtain the important information about the induced rotor test current vector from the stator voltage vector after the power frequency component has been filtered out. Figure 4.9 describes the method to isolate the rotor test current vector from the measured voltage. The approximation is valid if the test frequency is sufficiently high and the operating frequency, p of the flux angle to be measured is not too high. These conditions are normally met in the low flux frequency range. There: AVu=Ai~ sdq quxs + (—Ai ~ I,) + Aisfic’jLSI + (—Air&fi.r,)L,] (4,1) rdc'j According to equation (4.1) the voltage vector consists of four terms, namely the ohmic and leakage inductive voltage drops of Aisaq and (“Air&a)' The term that is presently in the fundamental measuring method can be found as term 2), multiplied however by r,, If the items 1), 3) and 4) were to be zero, the determination structure could be the same as the method with the rotor measurement. The terms 1), 3) and 4) could be reduced to zero by compensating actions on the stator voltage vector 40 but this would require the knowledge of some machine parameters. The influence of these terms can be cancelled by enlarging the determination structure. No action has to be taken to eliminate term 1) of equation (4.1), because the imposed 13.ng1 is always equal to zero, so that the important second coordinate of the test voltage vector is not influenced by term 1). Unfortunately, the terms 3) and 4) drastically change the test voltage vector, because these two inductive leakage voltage vectors are perpendicular to the previous ohmic ones 1) and 2). The final voltage vector, consisting of all terms, cannot therefore be used. There is, however, a very effective countermeasure to this problem. The pulsating stator test current vector Aisaq can be decomposed into two vectors with equal amplitude, which are rotating with respect to the estimated flux axis, in opposite directions: the positive-sequence vector, rotating with frequency 6r , and the negative-sequence vector with frequency —&. The positive-sequence vector is obtained by a rotation over —&, the negative sequence vector by a rotation over +61. The decomposition of the voltage vector is used to obtain term 2) of equation (4.1). This is shown in figure 4.9 by e11“ and the Low-pass filters (LPF), yielding f'3 and 9“ respectively. The ohmic terms of the voltage vector in the positive-sequence and the negative-sequence system are equal, but the directions of the leakage inductance terms are opposite. This means that the 41 leakage inductance terms cancel each other out when the two systems are added and the resulting voltage (fa+ga’) only consists of terms 1)and 2) figure 4.10 of equation.4.1, multiplied by two. The second coordinate of this voltage vector, that is proportional to -Ais,~,, is the signal that should be used to adapt the estimated rotor flux angle in the u/i-model. When this mean value is equal to zero, the shifting angle 7 = 0 is equal to zero and the estimated rotor flux angle is equal to the real rotor flux angle for more detail see figures 4.11,4.12. Where vectors of f°and g". In conclusion, the aforementioned measuring structure is able to determine the flux angle at small flux frequencies and particularly at zero frequency by only using stator voltages and stator currents. The measuring structure, mentioned above, only functions satisfactorily if the machine is saturated. From the point of view of losses it is generally recommended to use such an operation condition when it is absolutely necessary. Besides, inadmissible voltages would result at high frequencies. Therefore, this measuring method is clearly an expedient which should help an already existing voltage/current model at low frequencies. 42 Vqu AVsdq 1 iSd' 0’"3 Isab , e-ii’ ' :igh e-ja :ow . - ‘ Motor * ass ~ ass 'sq H Filter Filter - or Al 8d Low a .e ja ‘3 e j“ Pass 1 Filter 0 _.r Motor 4—— Controller ¢ Model faz+galz or T &=2fif(test) Figure 4.9 Block diagram of simulation/actual implementation 43 Figure 4.10 Construction of f3' when parts 1) and 2) are available ---> a-axis Figure 4.11 construction of fa when parts 1) and 4) are available 1) ~ + a-axis 3) 98:2 IIIIII 4) Figure 4.12 Construction of 98’ when 1) and 4) are available 44 4.5 LIMITATIONS OF THE METHOD The method described, although promising at low frequencies, has certain limitations. a) Since it is based upon saturating a standard induction motor and by injecting a high frequency test-current, the power frequency has to be lower than the test frequency. This means the method is valid very close to the zero power frequency. An objective of this thesis is to investigate its accuracy as the power frequency is increased. b) Another obvious limitation of the saturation-based approach is field weakening operation. Robust tracking of saturation-induced saliencies requires operation at flux levels that are considerably higher than normal or rated. The maximum operational speed is then limited by core loss and/or stator voltage. Obviously, field-weakening operation beyond base speed is not possible. Therefore, to obtain wide speed range operation, including field weakening, the high frequency injecting scheme must be combined with a scheme suitable for high-speed operation like direct field orientation (DFO). c) The estimated rotor flux is sensitive to the angle difference between the estimated and the actual flux. When the difference angle is not too large, a value of the estimated magnetizing current would also result in large value of actual magnetizing current id, figure 4.13, thus maintaining saturation. If this angle is too large, it will result in loss of induction motor main-field saturation, due to the decrease in the excitation current id, Figure 4.14 shows that when the error angle 45 is large, even a large value of estimated magnetizing current will result in small value of actual magnetizing current id, thus driving the motor out of saturation. Hence, a technique has to be developed to keep the flux constant, at an operating point around the zero power frequency operation. The injection of high frequency in the saturated induction machine promises to be a viable and potential attractive means of achieving transducer-less field oriented control in certain applications requiring sustained zero and low speed operation. 46 Wd Wd Stator axis Figure 4.13 Saturated condition due to small estimated flux Wd ;Stator axis Figure 4.14 Loss of saturation due to large estimated flux error angle 47 Chapter 5 APPROXIMATED TEST SIGNAL VOLTAGE VECTOR 5.1 INTRODUCTION From stator voltage equation of the induction machine it is possible to estimate the rotor test current. The stator voltage equation has to be transformed to the rotor flux reference frame. At low flux frequency an approximate expression of the approximated voltage vector at the output of high pass filter is obtained, which is derived in the next section. This approximation is valid if the frequency (test) is sufficiently high; in addition, the operating frequency p of the flux angle to be measured should be low. The well-known voltage equation for induction machine are expressed as follows: — 7 an V = R . +——i“— 5.1 83 S 158 dt ( ) VSD =RS'YSD + dWSb (5.2) (It R7,, =0: R,.i,,, + ‘13:“ (5.3) CW7: v,,_o=R,1,B+ dt” (5.4) The stator flux linkages in the arbitrary reference frame x-y are: 48 ‘I’sx =‘I’I + Llsisx (5-5) vs, =w, +L,,isy (5.6) where ml is the leakage flux linkages. Rotor flux linkages in the arbitrary reference frame are:- wn, =w, +L,,i,x (5.7) w” =w, +L,,is, (5.8) The equations are given in the vector format. As shown, every vector variable has two components: the first component is parallel with the reference frame axis and the second component is perpendicular to the reference frame axis. The stator voltage equation is restricted to the stator reference frame because of the differential of the stator flux vector; the rotor current equation is however restricted to the rotor reference frame because of the differentiation. The flux equations are defined in the general reference frame. Before these equations are completed to obtain the approximated machine model in the rotor flux reference frame, the reference frame of the model has to be chosen. Some considerations about this are given in the next section. 5.2 CHOICE OF THE REFERENCE FRAME The reference of the model must be a coordinate system in which quantities in a steady state are at rest, i.e. in which all quantities appear as DC quantities. The direction of the stator or rotor current vector and direction of any flux vector may be considered as reference axis, because these vectors are rotating at the same speed, i.e. synchronously, with respect to each other in a 49 steady state. One should not choose the rotor axis or the stator axis as the reference axis, because all vectors are moving with respect each other to the rotor and stator in a general and also in the stationary operating condition. The second consideration in choosing the reference frame is the desired decoupling of the rectangular (Cartesian) coordinates of the stator current vector. This decoupling of the stator current components means that the two components can be controlled separately and independently of each other. This way a control strategy similar to the DC machine control can be achieved. Figure 5.1 shows some of the different reference axes that can be chosen. .. y . .-" .- .- .. D.- .u"..... .. a" . a" .I' Stator axis V Sa Figure 5.1 Different coordinates axes in AC machine modeling The flux linkage of the rotor windings, or abbreviated rotor flux, can be considered a central quantity because this flux is responsible for producing the current in the rotor windings (rotor current) and for producing the electromagnetic 50 torque which will be shown in the next section. Therefore it is reasonable to choose the flux axis as the reference coordinate axis. In the rotor flux reference frame the two-stator components are completely decoupled. This is not the case when choosing the stator flux axis or the air gap flux axis as the reference axis (however, simple measures can overcome this problem). This simple decoupling strategy is another reason to choose the rotor flux reference frame. 5.3 APPROXIMATED TEST SIGNAL VOLTAGE VECTOR USING FLUX LINKAGES The rotor flux appears in its own coordinates systems only with its value as its first coordinate; the second coordinate is zero. Therefore, the w,d=\]r, (wm=0) and hence the rotor flux can be written as: _ ‘I’rd _ ‘I’r “It'd —[\qu]—[ O] The stator flux is w, = (IVS, WWII To emphasize the coordinates transformation to the rotor flux references frame, the Cartesian field-oriented coordinate, parallel with the rotor flux is called magnetizing coordinates and the one perpendicular to the rotor flux vector, the torque-producing. it must be stressed that these coordinates (with respect to the induced voltage of the machine) do not correspond to the generally known reactive and active power components of the stator current (with respect to the 51 terminal voltage of the machine) which are used to determine the power factor at the machine terminals. The inputs of the current-fed induction machine model are the stator currents. The three-stator currents of the three-phase induction machine are transformed into an orthogonal two-phase system connected with the fixed stator. Inside the model the two-phase stator currents are transformed from the stator reference frame to the rotor flux reference frame. This way the magnetizing component and the torque-producing component of the stator are obtained. These field-oriented stator currents are the input variables of the current-fed induction machine model. Output variables are the rotor flux inside the machine, the slip frequency of the rotor flux, the angle of the rotor flux with respect to the stator reference frame (the field orientation angle), the electromagnetic torque, the rotor frequency, and angle of the stator terminal voltages. The equation system of the current-feed induction motor in a vector notation starts with the voltage equation (5.1-2) of the stator windings (in stator coordinates) and the voltage equation (5.3-4) of the rotor windings (in the rotor coordinates). The stator flux linkages and the rotor flux linkages are defined in equation (5.5-6) and (57-8). The total magnetization current i,,, is defined as the air gap flux divided by the main inductance Lm. Wm = Lmlm lm = Is-I-Ir 52 With the help of equation (5.5-8) an altemative magnetization current is defined which is valid in any reference frame: Wrm = Lmirm l,,,,=is+(1+o)i, Where 6: Lu/Lm is the rotor leakage factor. The rotor vector becomes a scalar in its own reference frame: __ ‘l’r Wt -[ 0] Transformation of the derivative of the rotor flux vector from rotor coordinates (equation 5.3-4) to rotor flux coordinates is done by rotating this vector over angle 0,, =p-0, (see figure (5.1)). This leads to: . _ _d_ COS 8d -sin 9d ‘I’rd _ 1 jgd ‘I’rd “(‘13) _ dt sin 9d cos0d \qu _ dt \lqu nd Eel“ = (.Ie’wej (2] cos 0d - sin 0,, dt where em: , srn0d cos0,, 53 O =ej°d In 0 9d \I’r with the help of the last equation, vector equation (3-4) yields in the field oriented coordinates: 616d . Wf = _Rrjr((XB) : —Rr.eledir(dq) 9d ‘I’r Wr = "'Rrird 9d Wr = "Rrirq This means that the magnetizing rotor current (i.e. the induced magnetizing current component in the vector windings) originates from the variation of the flux value and the torque-producing rotor current originates due to the rotation of the flux vector with respect to the rotor. The frequency 0,, of the rotor flux with respect to the rotor is called the rotor flux slip frequency. 54 The rotor flux magnitude is calculated by integrating the \il, = —R,i,,,: Wl=hhm The equations Wm, = L,,,i,m and l,,,,=is+(1+o)i, yield the relation between the rotor current and the stator currents: ‘ird = 1 isd—fi 1+6, Lm . 1 " = —_ Gs ) M 1+ 0, q The above equations and in addition Iii, =—R,i,d and 9N, =—R,i,q are the central equations of the current-feed induction motor model. When the rotor flux slip frequency is added to the rotor speed, the rotor flux frequency with respect to the stator is obtained: P+éd=ér The frequency is integrated to obtain in the field orientation angle p: p=l¢ O" This angle is used to transform the input current vector from the stator frame to the rotor flux reference frame: [trellis] 55 where e_,-,, : cos0d sin0d —sin0d cos0d The equations mentioned above belong to the equation system of the current fed induction machine. 5.4 APPROXIMATED TEST SIGNAL VOLTAGE VECTOR USING ROTOR FLUX AND STATOR CURRENTS The stator voltage vector is calculated from the estimated rotor flux and the measured stator currents in the field oriented coordinates. The calculation starts from the stator voltage equations. The voltage equations V3,, Rsisa + dztsa , V8,, = Rsisb +2331 the stator flux linkages in the arbitrary reference frame wsx = w. +L,9,is,,,\|1Sy =w, +L1sisy and the rotor flux linkages w”, =w,+L,,i,x, my =w1+L,,is, in the arbitrary reference frame yield the following equation: — 7 d . . Vsrab) = Rs.rs,a,,, + a; (anb) ‘ LrI "r(ab) + LIS'ls(ab)) This equation is transformed to rotor flux coordinates: _ - d ' . . R(p)vsld<1) = Rs'elp'lsNCI) + E[elp'(wr(dq) '- I"I'I'Ir(dq) + l'IS"s(dq) ):| 56 R(p)vs(dq) = Rs flip js(dq) + 9") '(TV—rwq) - Ln 'ir(dq) + LIs ~is(dq) )1" fl , . I" _ . . P-e’pe 2 -(\Vr(dq) - |-rI -'r(dq) + I-Is -'s(dq) ) After rotation of -p, this yields: .1! _ o 7 _._ . . . J_ _ . . V5,...) = Rs"s(dq) + vr-Ln- I WON Lls- '5(dq)+ 9-6 2 [Wr - Lrl-'r(dq) +I-Is- '8(dq)] Split into real and imaginary components, this equation yields: — 7 L d. d . " . ? Vsd = Rstd + w,——L,,.—I,d +Lls—.lsd —p. -L,,.I,q +L|s.lsq dt dt — 7 d . d . ' . ? Vsq = Rstq -L".Equ +L|s 8?qu + p.[\]l, - Lner +Lls- Isa] The above equation can be analyzed from a different prospective: The well-known voltage equations for induction machine are expressed as follows: — 7 d— .— V..=R..u..+ ‘5,“ —Iw~v.. _ , aw ,_ Vsq = Rstq +7m+ )0)qu (Wm M =0=Rf + rd r'rd dt - Kw- (WW—rd 57 _ _ d— V,q=0=R,.i,q+ “’“i + K03 - (or )qu Stator flux linkages: \Ilsd = Lsisd + Lmim \[lsq = Lsisq + Lmirq Rotor flux linkages: \l’rd = I-misd + l-rird qu = I-misq 1” Lrirq Considering the stator and rotor flux linkages for the rotor flux oriented model, that is w,,,-—-0 the stator equations can be expressed as: . R+L . 'Sd=_(; rplrd 31L") i 3:, sq L rq 58 R,Lm2P V = +oL Pi + sd PS I s)}sd Lr(Rr+LrP) isd _m \I’sq Vsq $s 1' (GLS)P} isq - 0) ‘I’sd Where P is the derivative operator and oLs is the transient inductance. At zero or low stator frequency, where the magnitude of (o is quite small, mwsq(<>Ls. & Ln, hence L,,, at test frequency can be neglected. Hence oLs can be further simplified as: L O'Ls = LSI + Lr|[L——E-|: m ]3L5|+Lrj Similarly considering the rotor equations the induction motor, a dq-axis impedance diagram can be presented in per phase equivalent circuit as: AIS Rs 1.035013 Rr IOJIO'Lr AVS :j; jCIXLm Aimr At zero stator-rotor frequency and magnetizing type conditions Lm is very high and can be neglected. Therefore the per phase induction motor machine equivalent circuit can be redrawn without L,,. at the test frequency. Ais Rs jQI-SI Rf Air ijN 60 The diagram leads us to the following stator per phase equation, with AVs as the applied two phase stator voltage and Ais is the stator test current and Al, is the induced test current in the rotor windings. Moreover, in a mirror image of the test signal synchronous frame of reference about estimated the d-axis, the voltage equation is Subtracting the two voltages As evident, the component on the right-hand side (Ai,R,) of the above equation can be used to directly give information concerning the displacement angle 7. The above equation approximation is valid if the test frequency is sufficiently high and the operating frequency [5 (mm) of the flux angle to be measured is not too high. These conditions are normally met in the low flux frequency range. 61 5.5 APPROXIMATED TEST SIGNAL VOLTAGE VECTOR USING VOLTAGE MODEL Vsb = l-abF’ Rs 1‘ stp l-abP LmbP isb (5.9) The above equation 5.9 parameters are derived and explained in chapter 3. In this section the given derivation is used for simulating the approximated test signal voltage vector. The model was simulated but has coupling effects and assumptions that can not be realized in real time applications. To overcome this problem the equation needed to be de-coupled to make the simulation compatible to the real time application. The vector components in equation 5.9 are detailed in chapter 3. Lsa=sz+Lma st=LsI+Lmb Lma=Lo+chos(2u) Lmb=Lo-L2 005(2ll) =L2*sin(2u) Where Lo=(L+L,,,)/2; L2=(L-L,,,)/2; and dFF'I L = _ dFmrl 62 limrl Lma=L cos(2p)+L,,, sin(2p.) Lmb=L.cos(2p)+L,,. sin(2u) Lm=LrI+Lma qu=Lr|+Lmb L,=L,I+Lm Ls=LsI+Lm Then the voltage equation become: Vsa1 Rs 0 0 O “Fisa- FLsa Lab Lma LabW -53. = 0 Rs 0 0 dfsb + Lab st Lab Lmb . {Sb 0 (Dr-[4m Rr (Dr-LI Ira Lma Lab Lra Lab fra _-co,.Lm O —C°r-Lr RI‘ _ _lrb_ LLab Lmb Lab Lrb, _lrb_ Splitting them in stator and rotor equations: :— . u is. is. [Vsa]=[Rs O O 0].Isb +[Lsa Lab Lma Lab ] {sb Vsb 0 Rs 0 0 {1'3 Lab st Lab Lmb {ta _ll‘b_ Lll'b_ F-iSa-- O O O=[ 0 (0er Rr (DI-14} Isb +[Ilsa Lab }[Fsa]*|:Lra Lab:H:Ira] '4’)er 0 ‘err Rr lra Lab Lmb lsb Lab Lrb lrb _lbe 63 which gives: Isa o o [Vsa]=[Rs 0 0 0].isb +[Lsa Lab].[isa]+|:Lma Lab Hire] Vsb 0 Rs 0 0 Ira Lab st isb Lab Lmb irb _‘rb_ . ' [isa' . ‘ [im]=[L.. LabrI[ o as... R. aflysb {1... Laws], irb Lab Lrb ‘0er 0 -err Rr ira Lab Lmb isb . 3th- In the above model the states are the rotor currents. The rotor currents (isd, isq) in the rotor flux reference frame are the inputs, and are then transformed to the stator reference frame (isa, isb). Using the Matlab-simulink the stator voltage equation is estimated and was used for calculating the test signal at very low flux frequency, see figure 4.9. Chapter 6 SATURATED MODEL PARAMETERS-SIMULATION Computer programs were developed to simulate the limitations of the scheme used for the project. Basically there are two methods in computing the transient performance of ac. machines; either the currents or the flux linkages can be taken as state variables. When currents are chosen for the saturated model, differentiation of inductance with respect to magnetizing current arises, and when flux linkages are chosen it does not. To simulate the control response of the field-oriented control drive systems at zero or near zero fundamental frequency. We Inject a high frequency test current in the estimated d-axis of the saturated induction motor model. The machine parameters used for the simulation were different from the machine to be used for the real time application. To simulate the phenomena in the induction motor which take place due to saturation, a large magnetizing current is used to create flux levels significantly larger than the nominal rated flux. The saturation magnetizing current graph, figure 6.1, indicates that in order to obtain values in excess of 1.3 to 1.5 times the rated flux requires magnetizing currents of more than two times the rated current. Hence, for the project analysis the flux obtained with ids approximately 150% o f the rated current was used. 65 6.1 INCREMENTING OF INDUCTANCE IN SATURATED MODEL Including of the saturation of induction motor model in the field oriented induction machine modeling requires of knowledge of the motor saturation curve. Therefore, the saturation curve was first plotted by simulation of unsaturated model. Figure 6.1 illustrates typical magnetization characteristic for the induction machine, showing the nonlinear relationship between the rotor magnetization current and the magnetization flux linkages ‘Pm, used for this project. This magnetization curve was obtained by using the parameters of induction machine given in [13-14]. The unsaturated area was approximated to match the linear parts of the machine model. The same parameters of the machine were used for simulation. 66 er Chord-slope (LI-ll " Tangent-slope Operating point Air gap inductance (Lmo) I" . Imr l f/f’ : Lm / o Imr V |mo Figure 6.1 Magnetization curve 67 in a current fed field oriented induction motor, isd (at steady state equal to i,,,,) is the magnetizing current and is a known variable. Figure 6.1 clearly shows that the high flux levels predicted by the unsaturated model cannot be achieved when the motor is saturated, i.e. operated well above the knee of the curve. The variation in magnetizing inductance Lm Jig—"(l (also called cord In! . . . . . d Inductance) and the vanatIon of the dynamic Inductance L=—(J1-|\!L""|l (also called lmr tangent inductance and is the first derivative of the magnetizing curve) and, also the air gap inductance L,,,o (unsaturated model inductance) are plotted in figure 6.1. These inductances can be treated as the known parameters derived from the magnetization curve. It can be seen from the figure 6.1 that in the linear part of the magnetizing curve, L=L,,,=L,,,o_ The two inductances Lm and L take into account the fact that in general im, is continuously changing due to injected test frequency. For saturation induction motor model, Lm and id, become functions of the d-axis magnetizing currents, id,3 and id,. The field orientated motor model aligns the rotor flux with the d-axis. Thus to a first approximation, saturation will occur in d-axis, but not in q-axis. To reflect this in the model, the saturation value Lm was only used in the q-axis calculations. The reason for choosing L and Lm, for the saturated motor model can be further elaborated. From figure 6.1 it seems clear if we consider an incremental change which results in a change in the amplitude of the mmf wave. The 68 resulting flux wave amplitude is a nonlinear function of the total mmf (steady state plus incremental change) and the chord slope reactance will not correctly express the change. Instead, the tangent slope to the magnetizing curve, identified as the “transient saturated inductance“ gives the appropriate relation between the change in flux amplitude and the change in mrnf amplitude. Therefore, in the saturated model of this thesis, for incremental current variations which result in change of saturation level, the tangent slope inductance or “transient saturated inductance” is employed. For incremental current changes which effects only the phase of the flux as well as for terms proportional to the operating point flux (speed voltages), the chord slope steady state inductance is used. Moreover, in case of the d-axis, the flux ‘Pmdis is equal to ‘Pm, the instantaneous amplitude flux. In general, this component of the flux will be in the vicinity of or above the “knee” of the magnetizing characteristic, where saturation becomes important. The magnetizing inductance is effectively the transient saturated inductance, the slope of the tangent of the magnetizing characteristic at the operating point. It can be imagined that the operating point continuously moves along the saturated region of the magnetizing characteristic during the dynamic process. The corresponding tangent at the operating point continuously changes its slope as well. Therefore it is simply necessary to incorporate the non-linear magnetizing characteristic itself into the d-axis portion of the dq-model. The above statement can be summarized as: that the component in line with the flux (y-axis) tends to change the saturation level and its analysis requires 69 use of the tangent slope inductance. The other component (x-axis) and all steady state terms use the normal chord slope inductance. 6.2 SATURATED FLUX MODEL From the discussion in the previous section, it is clear that due to the saturation of the main-flux paths the magnetizing inductances in the direct and quadratic axis are different, and thus the self-inductance of the stator windings are also different. Similarly, the self-inductances of rotor windings is also different. For simulation, the system of this project is an indirect field orientation scheme, shown in figure 6 2. The main assumptions will be those used during the derivation of the space-vector equations for linear model. The magnetizing curve in figure 6.1 shows that the high flux levels predicted by the unsaturated model cannot be achieved when the motor is saturated. Hence the new flux model (saturated model) requires modifying the flux reference trajectory to also account for saturation. If this is not done, the control effort can easily command more voltage and current than the inverter can supply. The equations in the next page is the saturated model. 70 where 71 Tr ‘ ‘ IN Wm: imr . 4 1 __p I“ 1 + 1:: P A Figure 6.2 Field-Oriented Saturated Induction Motor Current-Fed Model 72 6.3 FLUX MODEL UNDER DYNAMIC AND STEADY STATE CONDITIONS Since the flux is dynamically varying in amplitude, it must be accurately tracked to ensure that field orientation is achieved. The saturation model, which predicts the level of flux, is therefore important. In this section the saturation model is discussed, which is used for the simulation to study the limitation of the proposed scheme. The assumptions on which field oriented flux model equations are based, are essentially the same as those for the unsaturated two axis model except that the main flux saturation in the flux axis (d-axis) is incorporated. As can be seen a subtle difference between the two models exists with respect to the division of the flux into leakage and magnetizing components. In the conventional model this division is actually quite arbitrary; any division whatsoever can be assumed and completely equivalent model results if the remaining parameters are properly evaluated. This is no longer true for the saturated model and, in principle, the division of leakage must be known to obtain an accurate representation. The effects of the saturation of the leakage flux paths are neglected and only the effects of the main flux saturation are incorporated in the analysis. In this thesis the correct calculated value of leakage inductance is treated as a constant value, both for stator and rotor leakage inductance, which has secondary effect and has not shown much effect on the simulation results. Also, it’s clear from figure 6.3 that the flux linkages in the saturated model are not much different from each other. Moreover, the stator leakage inductance (L3,) and the rotor leakage 73 an Sig 5.4 is, i If“ FL inductance (L,,) are small (less than 5 percent of the magnetizing inductance) [22]. Since L3=Ls.+L,,,; L,=L,.+L,,, ; and Ls.< d ‘Prd=‘Pr Figure 6.6 Vector of rotor current and flux in a field-oriented induction motor. 77 6.5 CONCLUSION: Field orientation control provides flux only in the d-axis, it can be assumed that saturation only occurs in the d-axis. Hence only d-axis saturation is used for the flux model and for calculating the fundamental rotor current components for further processing or calculating the rotor The motor flux saturated model includes both L,n (chord inductance) and L (tangent inductance). Due to saturation, the fundamental rotor current uses Lm (chord inductance) for both d and q-axis of the rotor current components. By injecting a high frequency test current in the d-axis a continuous dynamic condition is created, which leads to the determination of the rotor flux position. Test rotor currents, due the saturation effects, produces different factors k, and k2 as given below. These factors are independent of the test frequency and are valid at around zero fundamental power frequency: Aim _—kllsd Aim— kzisq where L L 1 1 k, - - - L L, Lfl +L 1+ rl 1+ rl L tanB Lm Lm 1 1 k2 :—:————: — L Lr L,,+L,, 1+ " 1+ " L tano 78 Chapter 7 SIMULATION RESULTS 7.1 TRACKING THE DISPLACEMENT ANGLE (7) Two different sets of simulation were run in order to evaluate the motor performance under the proposed scheme: a) It was assumed first that the motor rotor currents could be measured, and compared to the stator currents. A partial model of the proposed scheme was used, as shown in figure 7.1. b) The estimator method was simulated as it is implemented in the experiment. This complete scheme has already been discussed and shown in figure 4.9. Figure 7.2 presents the results of simulation and verified experimentally. For simulation and on line implementation different parameters motors were used. In both the cases, it verifies relationship between the errors in the flux position, p —{5, and the resulting displacement angle, 7, between the applied stator test current AIS and the corresponding rotor current Ai,. Except for a dc offset, there is proportionality that can be used for correction of the estimated rotor angle. Figure 7.3 presents the results of a simulation where this angle 7, is used to drive a PI controller that corrects the estimated rotor flux angle. 79 The same measurements on the actual experiment were conducted on a 1/12-hp induction machine. The experimental results demonstrate that a trackable signal of the shifting angle in the test frequency exits which can lead the rotor flux estimation at very low and zero frequency. 80 l>0.5 6 :r :I ‘M ”g: Figure 7.1 Simulation model for saturated Motor 81 W 1 3 9mm :0}— IxO POW .0 $ \ \ .° N -0.8 1 1 1 1 -1 .5 -1 -o.5 o 0.5 1 1 .5 Difference Angle Estimated shifting angle 5 is) o .5 «h 95 a) Figure 7.2 The Error Angle Vs the angle between actual and estimated flux 4 f 30" ‘ 2Q” ‘ 0 _ - '2, Id : omsLQ Estimate ~ 3 \\ E _ h 1 I .9 (IF ‘ , a? ~2Ci Actual r - -30 ‘ - '40 \\/ ‘ ‘5 0.5 1 1.5 Tim2e 2.5 3 3.5 4 4.5 Figure 7.3 Using the angle 7 to correct for rotor flux estimation 82 72 7.2.“ orde cum Iaxi with and I This berm rotor angle One Shlfiir angle lineli ESiIm 5‘33"]: 7.2 LIMITATION OF THE PROPOSED METHOD 7.2.1 Loss Of Saturation In the proposed method, magnetic saturation of the rotor is necessary in order to create saliency. This saturation can be accomplished by applying stator current component, is,,, that is on the same axis as the rotor flux. As a result, the q-axis parameters in the slip frequency do not vary much (small change in L,,,) with Wm. However, the d-axis parameters i.e. the tangent inductance L (Lmth) and the rotor time constants in the rotor flux equations are functions of the flux. This effect leads to the displacement angle in the rotor flux reference frame, between the stator test current and the induced rotor test current. It is very important to understand that in the test magnetizing current in the rotor flux reference the shifting angle or displacement angle 7 depends on the angle difference (error angle) 8 between the real flux axis p and the estimated one {5. In other words the shifting angle is proportional to the error angle. The shifting angle and the difference angle have opposite directions and the shifting angle becomes zero when 8 is zero. The shifting angle 7 clearly indicates whether the estimated flux axis ,5 corresponds with the real axis or whether the estimated one is leading or lagging the real one. As explained in section 4.4, using the rotor current to construct rotor flux position shows basic consequences of the saturation effects. Due to saturation 83 the chord inductance and the tangent inductance are not equal, hence, the induced rotor test current vector does not have the same direction as the test stator current vector. As result of the difference in these two currents, the shifting or displacement angle y is generated. This angle will exist as long as the motor is operated well above the knee of the magnetization curve and the estimated flux axis 8 is not aligned with the real flux axis p (i.e. p¢p ). The angle will not appear if the motor goes out of saturation, even if the patp. It is important to note that the scheme presented in this thesis is based on the conditions that the motor is fully saturated. Simulation results revealed a limitation in the proposed scheme in that the estimated rotor flux is sensitive to the angle difference between the estimated and the actual flux. When the angle error is not too large, as in figure 7.4 a large value of estimated magnetizing current would also result in large value of actual magnetizing current id, thus maintaining saturation. If the angle error is big, it will result in loss of induction motor main-field saturation, due to the decrease in the actual excitation current id, Figure 7.5. Then, when the error angle is large, even a large value of estimated magnetizing current will result in small value of actual magnetizing current id, thus driving the motor out of saturation. Hence, a technique has to be developed to keep the flux constant, at an operating point around the zero power frequency operation. Figure 7.7 shows the variation of rotor magnetization current due to the increase in the displacement angle 7. The lower part of figure 7.6 shows the effect of the angle error, 8 , on the shift angle, 7, that is used for correcting the 84 estimation of the rotor flux position. When this angle error become large it was difficult to use the value of 7. Figure 7.7 shows how for a fixed value of isd command in the estimated flux frame, the values isd, i3,, and im, changed, leading to loss of saturation. For simulation the commanded isd was kept at high value to keep the motor in saturation for larger difference value. In actual implementation keeping the value i'sd beyond two to three times the rated value may leads to excessive losses and high current demands from the inverter. Hence, adding the feed back can solve this limitation of the system and the stability can be obtained. 85 Wd Stator axis \ r Figure 7.4 Saturated condition due to small estimated flux Illa ,Stator axis Figure 7.5 Loss of saturation due to large estimated flux 86 4.5 I I U U I I T I 4 __ fi 20, 4o 3. 60 Hz _ l 7 vs 8 Simplified Model 3.5 - we 3 in=10 3 . 20 5 - II T ‘Y vs 5 1 i Complete Model ' 2 '- I “=18 5 Hz - 1 .5 - - 1 - 20 Hz 40 a so Hz '4 10 Hz 0.5 / - O *1! _O 5 l l I l l l l l l O 2 4 6 8 10 12 14 16 18 20 Difference angle 8 between estimated and actual flux Figure 7.6 Effects of large angle error and increased test frequency on the shift angle, y. 87 ., I 2531?] 'Sd I isq I imr 22 18 16 14 12 t 1 Un-Saturated Region 10 - 8 1 _1 l 1 l I l l 4 0 2 4 6 8 1 0 1 2 14 1 6 1 8 I I I I I 8 verses i... in & i,,., Igd=19, Iq=1 6.0)r=1 Saturated Region '80 Difference angle 8 Figure 7.7 Variation in magnetizing parameters 88 7.2.2 Power Frequency Limits Since in the realization of the proposed method it is impossible to use the rotor currents, we rely on the effect these currents have on the stator voltage. We consider the stator voltage equation in the rotor flux frame of reference: 15 — 7 _._ . . . J— _ . . Vs(dq) = Rs"s(dq) + W: - LrI- 'r(dq)+ LIs- 's(dq)+ P -9 2 [Wr - Ln Jr(dq) + Lls-'S(d<1)] When operating at low power frequency, the rotor flux frequency p will be negligible and the values in the equation within the parentheses will have no effect on the stator voltage equation. Moreover, at test frequency Lm >>Ls. & L,,, hence L", at test frequency can be neglected. This effect leads us to the following approximate equation: V5,...) = Rs'is(dq) + W.- Ln- irrdq) + Lls- isrdq) This approximation is useful in extracting information about angle 7, and it is valid if the magnetizing test current frequency is sufficient high; in addition, the operating frequency p of the flux angle to be estimated has to be low. These conditions are met only in the region of small power frequencies. As explained in chapter 4, the quadrature component of the above-simplified equation directly gives information concerns the displacement angle 7. 89 7.2.3 Test Frequency Limits The analysis presented in chapter 4 for the relationship between stator and rotor currents is valid when the test frequency is sufficiently low. The top curves in figure 7.6 show the effect of saturation for a variety of test frequencies, under the simplification that these test frequencies are adequately low. Indeed, the results show little effect of the test frequency on the angle 7. On the other hand, when the complete model is used for simulation, the effect of test frequency is pronounced. As shown in the lower curves, obtained with the complete motor model, for the method to be valid the frequency of the injected test currents must be below 10 Hz. Section 7.2.2 and 7.2.3 impose two contradictory requirements on the frequency of the test currents: it has to be sufficiently low so that the test stator current will be reflected on the corresponding rotor current, and sufficiently higher than the power frequency so that these rotor currents will have an effect on the stator voltage. The two requirements mean that the proposed method is feasible only in small region of power frequencies near DC, and the test frequencies should be between 5 and 10 Hz. 7.3 FIELD WEAKENING Another limitation of the saturation-based approach is field weakening operation. Robust tracking of saturation-induced saliencies requires operation at flux levels that are considerably higher than normal or rated. The maximum operational speed is then limited by core loss and/or stator voltage. Obviously, 90 field-weakening operation beyond base speed is not possible. Therefore, to obtain wide speed range operation, including field weakening, the high frequency injecting scheme has to be combined with a scheme suitable for high-speed operation. Suitable method were investigated that will provide a smooth transition to high power frequency operation. The rotor based direct field orientation (DFO) technique is used, explained in chapters 1 and 2. 7.3.1 Selection of Scheme for High Speed Operation. The system analyzed in this thesis is capable of changing dynamically, i.e during operation of the drive, the reference frame of the test current injected controller without any change of the controller hardware opens new perspectives of the induction motor drives. Drives that have to operate over a wide speed range can combine now, with the test current injected controller, different control strategies. For instant, at low speed range or around zero frequency range the test current injected controller is set to saturated condition. At higher speeds and in the flux weakening area, DFO with rotor flux controller is preferable. In this way the best of the best schemes are implemented without additional hardware and software of the controller. 7.3.2 Rotor Based Direct Field Orientation Figure 7.9 shows the diagram of a rotor based direct-filed orientation. In this system, the stator flux is estimated form the rotor voltages and phase currents in the stator reference frame: ‘l’s = “Vas 'I'Rsis)cIt 91 L . Wr = L—rW’s ‘ 6Ls's) m p = atan-‘L’Q is the rotor flux angle in the rotor flux reference frame. ‘I’ra The success of rotor based DFO depends on good estimation of the stator flux. The stator flux is obtained by integrating the phase voltage minus the voltage drop in the stator resistance. In the implementation of online system the dc offset in the voltage and current minimized by using the band pass filter and digitizing it using bi-linear transformation. Further, to maintain the accuracy of the estimated flux quantities, correct values of machine parameters are needed. In particular the stator resistance plays a crucial role in the stator flux estimation at low speeds, it is important to identify the correct value of this parameter. 7.3.3 Smooth Transition From a saturated magnetization curve and vector diagram one can derive that a change of the reference vector also requires a change of the commanded value of the flux (i'sd). Otherwise the motor will be operating in saturated mode and this would lead to high losses in the system and inability of the inverter to provide the required voltage. To cope with this problem one can calculate the two different schemes every sampling cycle. Due to the high processing speed of the processor (see chapter 8) the two controllers can be operated sequentially using the same routine for both schemes. Doing so, both reference frames of interest processor are in stand-by. The input command of the controller for the slow speed and the higher speed value can be calculated from the rotor flux speed or comparing the torque producing current components. However, the two routines 92 have smo igui this The of ti lhe‘ have to be provided in order switch from one reference to another. This way the smooth transition in simulation and on line implementation can be achieved see figures 7.8. The matlab simulink block diagram is shown in figure 7.9 used for this thesis for smooth transition from the saturated model to the rotor based DFO. The smooth transition could not be achieved properly and requires more analysis of the transfer technique. The system transfer tested several time, in most cases the transfer process was not stable. 0.3- .. j From proposed 0.4 - §\x Rotor based DFO Cos(Rho) O -1 L L 1 1 1 "" i 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (sec) Figure 7.8 Transition from DFO to Estimated Error method 93 i“. el" #2.. ,e‘li H High 640, Low fez _ Pass Pass , . - , T" Motor 41—. . . _— Isq % FIlter FIlter AIM (I L . ow + . la a ’e la 9 9 Pass a'2 _, v Filter 9 0 3mm ___ Motor ¢ Controller 9 MOdeI f82+gasz or '4 p=atan(‘Psq/‘Psd) T ? =21!f(test) W _’ Transform I to Rotor ‘Psb=I(Vsb-isbRs)d/dt ' Flux in Stator RF Figure 7.9 Switch from saturated model to DFO simu-link block 94 Chapter 8 EXPERIMENTAL SET-UP 8.1 INTRODUCTION Real-time computing is an important area of computer engineering due to the fact that computer systems must interface and deal with the real world, where certain time constraints are often present. Real-time systems must generate the desired outputs from given inputs, but the time at which these results are produced and delivered is of equal importance. The computer processor handles this task. Real Time Lunix is an extension to the Linux operating system, which allows for the execution of real-time tasks. It uses an ingenious technique to circumvent the apparently inherent non-real-time nature of the operating system. With RT-Linux we can take total control of the PC (we used PC because for the moment there is no implementation of RT—Linux for any other architecture) as for the case of MSDOS. During a real time task it is possible to access all the ports of the PC, install interrupt handlers, and temporally disable interrupts. The advantages of using PC hardware in embedded systems are by now well known. In contrast to much hardware developed specifically for the embedded market, PC hardware is mass-produced, easily available, and cheap. 95 We can expect interface boards such as analog and digital l/O boards, network interfaces, and image acquisition and processing boards to cost more than twice as much when designed for the VME bus as for one of the PC buses. When field orientation is used the induction machine can be controlled to provide high dynamic performance. To achieve this performance, flux angle has to be calculated both fast and accurate. During a short cycle time the complete set of real-time calculations has to be performed. This set of calculations can be very large when it embodies a model of the induction machine, the field- orientated control model, speed and/or torque controllers and parameter estimators. Until 15 years ago, a sampling time (which is also the real-time calculating time step) that was small enough was not possible with the real available microprocessors. For this reason until recently often analog controller were used for the field orientation control of AC drives. The increasing use of PC hardware is one of the most important developments in high-end embedded systems in recent years. Hardware costs of high-end systems have dropped dramatically as a result of this trend, making feasible some projects which previously would not have been done because of the high cost of non-PC-based embedded hardware. But software choices for the embedded PC platform are not nearly as attractive as the hardware. One can choose DOS, with its well-known limitations; Microsoft Windows, with its lack of real-time capability; or one of the high-end real-time operating systems, which are expensive, proprietary, and mostly non-portable. The Linux operating system 96 presents an attractive alternative to these options, having none of the above disadvantages. RT-Linux is used for this thesis. Using pentium processors at 400 and 450 MHz and the RT-Linux environment the gap between simulation and experiment can be closed. The System is much faster, reliable and cheaper especially in data processing, than the DSP system. The necessary calculation and input/output speed of real time simulation can be achieved and the performance of the analog simulator can be matched. The analog part should consist of the interface between the PC- processor and analog signal from the machine (A/D converter for voltage and current measurement). The advantages of using RT-Linux in a PC processor in particular as opposed to DSP are: 0 higher reliability, because no boards and wire connection is inside the computer. . flexibility of models and control structure because of the high-level software implementation; . no debugger and measured data transfer interface program are required. Data is directly stored for processing with MATLAB and pnnfing. - easy change of model parameters and inputs (software); . output of any signal to media: hard disk, floppy drives; after saving the data all kinds of signal processing can be performed without designated software. 97 no standard configuration files are created to perform initialization of the system software (timers, interrupt vectors, l/O cards, etc). 8.2 EXPERIMENTAL CURRENT CONTROL HARD WARE SET-UP 8.2.1 Experiment Drive Setup The drive setup is shown in figures 8.1 to 8.3 are explained below. In case of simulation, part of figure 4.9 is used. In the experiment the same induction models are used to control the real drive system. 1. The experiment drive setup consists of a PC-based controller using Linux operating system with analog to digital (A/D) data accusation system, for induction motor control, as shown in figure 8.1. A 3-phase, 1/12 HP, 60 Hz induction motor is connected through a voltage controlled current regulated hysteresis-PWM inverter. The three-phase hysteresis current control PWM inverter is composed of 3-phase, 60 Hz, 208 VLL, AC/DC converter and a 10 kHz IGBTs switches. The three-phase motor, stator voltage measurements and stator current measurements are done by using voltage transducers (W5) and current transducers (CTs) as see figure 8.1. The analog output signals from W5 and CTs are transformed to the digital signals are obtained by using a 12 bit A/D converter. The 12- bit AD 7874 converter has B-usec/channel conversion time and has 98 four-channel simultaneous sampling capacity. These characteristics are ideally suited for use in the induction motor vector control. Six digital signals from the PC-based controller are fed to the inverter IGBTs switches, through the switching control board. These digital signals are produced after comparing the estimated current values with the reference current signals. Matlab is used to display the measured or simulated voltage, currents, flux, in a rotating or stationary coordinate frame. Magnetic current sensors do the three—phase current measurement. 99 Six Dldtal Sim IGBT PC Drive C II Circuitry ontro er . (Hysteresrs) Invener lad.......... ... .. isn, CT A/D Transformation conversion I PT Figure 8.1 Experimental set-up 100 From Motor Inputs Transducer Vac, vbc. Issi'h [ 12 Bit,4—Ch.,29 KHz, Simultaneous A J 12-Bit Digital Signal [ ngh Speed Bidirectional Parallel Potts 4| Hadware l [ Sample v.,,, Vm I... In, and trim the offset I Software I l l Ic ='-|A-la I Vf’VACTVBC Test Signal Frequency Test Signal Angle <1 PC (RT Linux) Hysteresis Error Between Actual and Estinsted Flux lGBT Switching Control High Speed & Vay Low Speed ................................................ Unsaturated & 3mm, Digital switching ll iii . Inverter Figure 8.2 Hardware and software schematic of the experimental set up 101 l Motor Inverter l TransducerJ Analog Signal V”, vb! '.o I" raw CH. 16 BitAto DJ W-Bit Dloital Slanal J [ 8-Bft High Speed Bidirectional Parallel I $.. /""""" Sentplev.,vnl..lnandtrfmtheolfset Determine Vab and lo l Compare the Currents \/\PC (RT Linux) 3' 1 Filter m I.d I. M v i 9h 2 lo =|A+|e VA8='VAC+VBC Vas Ivnb‘ Vida sw- at \I’ await!!- Horde Inverts Figure 8.3 Signal flow in the experimental setup 102 8.3 HYSTERESIS CURRENT CONTROL The current source can be a voltage inverter hysteresis or PWM controller. In the hysteresis the current controller upper and lower band levels are defined relative to the reference value of the current (see figure 8.4) and the inverter is used to ensure that the actual stator current is limited to between the hysterisis bands. By defining narrow hysteresis bands, it is possible to ensure tight control, but this demands a high switching frequency from the inverter. The actual current contains harmonics, which produce high-frequency torque ripples. These are filtered out by the inertia of the machine so the speed of the machine can almost be free from the effects of these ripples. Compared to the PWM current controller, the hysteresis current controller reacts almost instantaneously to changes in the reference values of the current, and thus the time lag is very small, whereas in the PWM current controller the switching frequency of the inverter is preset and it is easy to determine the time delay between the time the reference changes and when corrective switching action is performed by the current controller. Impressed stator currents supply the stator windings of the induction machine. The currents are obtained from a current-controlled switching transistor inverter with a high switching frequency. This application is similar to the application of annature current control in a converter-fed d.c. drive. The main advantages of this type of operation is that because of the impressed stator currents, the effects of stator resistance and leakage inductance on the drive dynamics are eliminated and the motor interaction is simplified. A time delay of 7us was introduced in the hardware of the inverter used for this thesis. This delay is sufficient to avoid the short circuit in the inverter, while 103 keeping the high switching frequency as demanded by the upper and lower current limits. The signal flow diagram in figure 8.4 shows three hysteresis controllers, one for each phase. Each controller determines the switching-state of one inverter leg such that the error of the corresponding phase current is maintained within the hysteresis band. The width of the hysteresis is iAi. The control method is simple to implement, and its dynamic performance is excellent. There are some inherent drawbacks which are not in the scope of this thesis. Encoder was also connected to find the actual flux angle for estimating the error difference between the actual flux and the created angle difference. 104 Current band Figure 8. 4 Hysteresis current control: (a) signal flow diagram; (b) basic current waveform. 105 8.4 DIGITAL TO ANALOG CONVERSION A very important issue when using digital PC based processor CS is the analog to digital conversion of the measured signals, e.g the induction machine voltages and currents. The A/D converter used in this thesis is AD7874 a four- channel simultaneous sampling, 12-bit data acquisition system. The part contains a high speed 12-bit ADC, on chip reference, on-chip clock and four track/hold amplifiers. This latter feature allows the four input channels to be sampled simultaneously, thus preserving the relative phase information of the four input channels, which is not possible if all four channels share a single track/hold amplifier. This also, makes the AD7874 ideal to sample multiple input channels simultaneously without incurring phase errors between signals connected to several devices. The AD7874 is also fully specified for dynamic performance parameters including distortion and signal-to-noise ratio. 8.4.1 IIO Board One bi-directional parallel port on-board with options to upgrade to 3 ports and support IRQS, which eliminates system conflicts. The PC processor used in the control system of this thesis is the Pentium II 400 MHz. It is a 32-bit floating-point unit, a 16-/24-bit fixed-point unit, on-chip memory, and flexible serial and parallel input/out ports. It has the capability of to support wide variety of computation-intensive large numbers of repetitive mathematical operation applications. The arithmetic unit, allows the device to perform up to 25 million floating point operations per second (with clock rate of 106 400 MHz). This performance was sufficient to satisfy many of the real time algorithms used in my thesis. 8.4.2 Software: In order to perform real-time simulation and control in an accurate way, it is necessary to calculate the complete machine control process with small time steps. In this thesis the interrupt frequency was high. Hence it was preferred to program the RT-Linux in the C language. A library contains programs for analog and digital inputs and output, as well as C language program to generate a MATLAB data files are given in appendix B-1 and B-2. Figure 8.1 verify the experimentally the relationship between 7 vs 5 which leads to the estimation of the rotor flux angle. The encoder was used to find the flux angle using indirect field orientation. -o.e - 1 . . -1.5 -1 -o.5 o 0.5 1 1.5 Diffrence Angle Figure 8.1 The Error Angle Vs the angle between actual and estimated flux 107 Chapter 9 CONCLUSION In this work we presented a promising solution to one of the fundamental problem in the induction machine speed control at zero flux frequency, with some limitations. The zero flux frequency is not stable with derivative feedback nor with flux magnitude estimation. Chapter 4 introduced an alternative method that does not replace the existing voltage-current model, but supports it At zero (or around zero) rotor flux frequency, the stator based DFO and IDFO using voltage-model and current-model are at the stability boundary. The risk of a steady-state flux angle and magnitude error exists if the flux value is not accurate in comparison with the flux command value. This is explained in chapter 1, for the case of a de-tuned but constant main inductance Lm (unsaturated). An improvement of this situation is the operation of induction machine in the saturated condition. This is only necessary in the zero frequency or very low frequency area. It should be restricted to the area to minimize the extra losses caused by the saturation. The low flux frequency is a small operation area to be solved: the operation area around zero flux frequency where saturation could leads to a solution. The scheme presented in section 2.5 indicates that the induction motor speed control scheme at zero frequency is devised in this work can be successfully implemented to solve the problem in the AC machines. 108 The derivation of the saturated model and assumption of simplified induction motor voltage equations in Chapter 3 and chapter 5 and are the major equations used for the simulation of this thesis. A sensor-less method, which is based upon saturation effect of the induction machine, is used to enable a stable flux determination near zero frequency. Our scheme does not suffer from the integration problem at low frequency. We investigated the theoretical aspects of the scheme. The algorithm of high frequency injection presented in section 2.5 is applied. However, our design procedure and analysis are fundamentally different from those of [3] due to the use of a rotor flux model and not at the stator flux oriented model. The algorithm used to control the induction motor at zero frequency is to inject high frequency test current in the d-axis of the saturated stator current. This technique is mostly machine oriented and is now gaining momentum for using it for controlling the AC motors. This high-high frequency magnetizing current injection method is meant to support, but not to replace the stator based DFO and lDFO techniques. It is due to the reason that the DFO and IDFO suffers from the integration problems at low frequency. In proposed scheme the high frequency test current passes through integration process. Its frequency remains high and constant during the filtering process, and hence does not suffer from the integration problem. Chapter 3 & Chapter 4 deal with saturated motor model control by injecting high frequency test current. Many important contributions have been made in [4]. However, integrating the motor design with high-test frequency, 109 make all of such attempts for special design motors and cannot be applied to any off shelf induction motors. In this thesis several techniques for estimating the rotor flux at higher speed operation and their performance at low frequency were reviewed. The Direct Stator Flux orientation (DFO) control system rather than the rotor flux (used only at low or around zero frequency) offers the additional advantages of more robust estimation of the flux and direct control of the stator voltage in speed below rated and above i.e. the filed-weakening region. In general, DFO requires more computing power to implement than Indirect Field Orientation, used for the zero or near zero frequency operation. As a result of the above study we laid the foundation or the development of the extension of our scheme to higher speeds. In this work we identified a direct stator based technique by using the DSFO, which is feasible for both below the low and high-speed operation of the induction motor. In conjunction with that we presented the high frequency limitations of the test injection scheme and the low frequency limitation of the DSFO. The hybrid system used is good from zero to high speed. The deviation of the main inductance Lm causes a steady-state flux angle and magnitude error due to saturation, as a result of additional inductance (tangent and chord), as explained in Chapter 3. However, in the case of saturation, with proper saturation curve this L-detuning is no longer problematic, as expected. The detuning of the leakage inductance L. has a very small effect 110 on the stability of the system: the simulation analysis with L. and analysis without L. yielded similar results with negligible differences. More over, the experimental results show the versatile digital contronata acquisition system based on RT-Linux with PC 400 MHz processor and A/D converter presented a good performance for both low and high-speed, filed weakened operation, which needed more computational time. This would bring a a very high speed operation and reduction in the price of on line embedded data acquisition system. FURTHER RESEARCH o The proposed system and the transition between this and the DRFO as the speed changes, has to be further investigated both theoretically and experimentally. 0 An interesting open question is to extend these results to more general class of AC motors. Also, the results and the technique used in this thesis can bring some ideas to control of electromagnetic operated devices, like linear motors, friction less bearing, etc. o A further important issue that is not fully studied in this thesis is the effect of parameter detuning. In this thesis almost all contributions are based on the assumption that the system parameters are accurately. known. In general, it seems that the operation of the machine in saturation has a positive effect on the parameter sensitivity of the field-orientated control system, especially at low flux frequencies. This appears to be caused by the fact that magnetizing current 111 variations cause relatively smaller flux variations in case of saturation. The positive effects of saturation (and its extra losses) are still to be analyzed. o It would be interesting to find adaptive extension of the contributions given in, especially for the most difficult problem of tracking control of the actual excitation current (isd). To keep the track of the flux angle at very low speed, the magnetization current has to be sufficient in order to keep the motor in saturation condition, irrespective of the angle between the actual flux and estimated flux. 0 Further research on the same subject should contain more details of the complete theoretical background of the high-frequency magnetizing- current injection method. Moreover, would be useful to optimize its practical utilization. o The rotor resistance Rr however has an important effect on the steady state, because the slip frequency is proportional to Rr, and on the dynamic behavior, because Rr is a parameter of its effects. That influence needs to be understood fully and examined for the saturated condition. 0 Stator resistance detuning has an effect on the steady state of the field-orientated induction machine. This effect is negligible at high frequency test current. The detuning effect on the stability is still a very important subject to be examined under the saturated condition. a The problems of using the DSP constraints of using the assembly language led to the use of an on-line system using PC based processor-using RT-Linux. This system can be further improved with high-speed PC processors 112 and using high speed parallel l/O ports for data acquisition and transfers. Improvements to the RT-Linux system can lead to more efficient and fast controllers. 113 APPENDICES 114 APPENDIX A A-1 FLOWCHART OF RT-LINUX WITH INTERRUPT ROUTINE Initialization If Interrupt Routine I 4 Clean Up Flowchart of RT-Linux Based System with interrupt routine 115 A-2 INTERRUPT SERVICE ROUTINE Enable Read b Read Channel 1 (voltage_AC - 12blts} (8-blts MSB-Lptt, & 4-bits LSB-Lpt2) 11 Read Similarly channel-2 to 4 are for voltage_BC, current_A, and current_B j v Disable Read (Disable Read is after each Enable read for each channel.) i Enable CONVST Disable CONVST 1 Program Calculation I Output to inverter I Output to FlFo User Process to Store Data Y IRO7 Hardware Interrupt sent to the computer when ND is complete Interrupt service routine 116 '"I h 2' Imam-r1 A-3 RT-LINUX INTERRUPT TIMINGS Table: Breakdown of time spent during one interrupt cycle using ND converter with RT-Linux 4us 5.1us 1.4us 29.9us A/D Communication. CPU Calculations Inverter Command CPU Free Time 33.4us Sps A/D Conversion Time INT Pulse-width Delay Total Interrupt Time = 50.4tts Note: Other minor delays in the A/D are introduced by pulse-width of l/O commands. 117 APPENDIX B B-1 RT-LINUX C-LANGUAGE PROGRAM FOR ON LINE SYSTEM The program is used for the Direct and indirect rotor flux orientation control program and the user data writing program (Appendix B-2). This program compiled by "make' and run by “mods" and stop by 'umods' commands. #define MODULE #define BAS E_AD DR ESS (1 27*0x100000) #include #include #include #include #include #include #include #include #include #define LPT 0x378 #define LPTS LPT+1 #define LPTC LPT+2 #define LPT 2 0x268 #define LPTZS LPT2+1 #define LPT2C LPT2+2 #define LPT3 0x280 #define LPTSS LPT3+1 #define LPT3C LPT3+2 #define LPT4 0x288 #define LPT4S LPT4+1 #define LPT4C LPT4+2 int ; //Define motor int variables constants and parameters double ; ”Define motor double variables constants and parameters void intr_handler(void) { control=controll0x01; // Pulse RD outb(control,LPTC); // Pulse RD current_msb_a=inb(LPT); // Read 8-bit MSB current_a from LPT current_lsb_a=inb(LPT2); // Read 8-bit LSB current_a from LPT2 control=control&0xFE; // Un-Pulse RD outb(control,LPTC); // Un-Pulse RD control=controll0x01; // Pulse RD outb(control,LPTC); // Pulse RD current_msb_b=inb(LPT); // Read 8-bit MSB current_b from LPT current_lsb_b=inb(LPT2); // Read 8-bit LSB current_b from LPT2 control=control&0xFE; // Un-Pulse RD 118 outb(control,LPTC); // Un-Pulse RD control=controll0x01; // Pulse RD outb(control,LPTC); // Pulse RD voltage_msb_a=inb(LPT); // Read 8-bit MSB voltage_a from LPT voltage_lsb_a=inb(LPT2); // Read 8-bit LSB voltage_a from LPT2 control=control&0xFE; // Un-Pulse RD outb(control,LPTC); // Un-Pulse RD control=controll0x01; // Pulse RD outb(control,LPTC); // Pulse RD voltage_msb_b=inb(LPT); // Read 8-bit MSB voltage_b from LPT voltage_lsb_b=inb(LPT2); // Read 8-bit LSB voltage_b from LPT2 control=control&0xFE; // Un-Pulse RD outb(control,LPTC); // Un-Pulse RD control=controll0x02; // Enable CONVST outb(control,LPTC); // Enable CONVST control=control&0xFD; // Disable CONVST outb(control,LPTC); // Disable CONVST ticks=rt_get_time()-zero_ticks; // Get time in ticks seconds=(double)ticks/1 193180; // Convert ticks to seconds ll Multiply the current MSB by 16 and add on the least sig. 4 bits of the LSB value cu rrent_dig_a=(1 6‘current_msb_a)+(cu rrent_lsb_a&0x0F); if ((current_dig_a&0x800)==0x800) current_dig_ =-(current.dig_a"0xFFF)-1; current_A=( (offset triming factor)*(double)current_dig_a); cu rrent_dig_b=(1 6*curre nt_msb_b)+(cu rrent_lsb_b&0x0F); if ((current_dig_b&0x800)==0x800) cu rrent_dig_b=-(current_dig_WxFFF)-1 ; current_B=((offset triming factor)‘(double)current_dig_b); // Multiply the voltage MSB by 16 and add on the least sig. 4 bits of the LSB value voltage_dig_a=(1 6"voltage_msb_a)+(voltage_lsb__a&0x0F); if ((voltage_dig_a&0x800)==0x800) voltage_dig_a=-(voltage_dig_a’\0xF F F)-1 ; voltage_AC=(offset trimming factor)’(double)voltage_dig_a+0.294138077413; voltage_dig_b=(1 6"voltage_msb_b)+(voltage_lsb_b&0x0F); if ((voltage_dig_b&0x800)==0x800) voltage_dig_b=-(voltage_dig_b"0xFFF)-1 ; voltage_BC=(offset trimming factor)*(double)voltage_dig_b-0.449866251504; System Equations // Current comparison Hysterisis if (current_A>(current_A_ref+band)) inverter=inverter&0xFE; else if (current_A<(current_A__ref-band)) inverter=inverterl0x01 ; if (current_B>(current_B_ref+band)) inverter=inverter&0xFD; else if (current_B<(current_B_ref-band)) inverter=inverterl0x02; if (current_C>(current_C_ref+band)) inverter=inverter&0xFB; 119 else if (current_C<(current_C_ref-band)) inverter=inverterl0x04; outb(inverter,LPT3); ”Ten out put data parameters name can be added. This number can be icreased. rtf_put(1,&seconds,sizeof(double)); // Push seconds into fifo ”can be used as standard rtf_put(2,&output parameter,sizeof(double)); // Push 12-bitvar_2 into fifo rtf_put(3,&output parameter,sizeof(double))i // Push 12-bitvar_3 into fifo rtf_put(4,&output parameter,sizeof(double)); // Push 12-bitvar_4 into fifo rtf_put(5,&output parameter,sizeof(double)); ”Push 12-bitvar_5 into fifo rtf_put(6,&output parameter,sizeof(double)) ; // Push 12-bitvar_6 into fifo rtf_put(7,&output parameter,sizeof(double)); // Push 12-bitvar_7 into fifo rtf_put(8,&output parameter,sizeof(double))i ” Push 12-bitvar_8 into fifo rtf_put(9,&output parameter,sizeof(double)): ” Push 12-bitvar_9 into fifo rtf_put(10,&output parameter,sizeof(double)); // Push 12-bitvar_10 into fifo int init_module(void) { rtf_create(1,16'sizeof(double)); // Create fifo for seconds rtf_create(2,16*sizeof(double)); // Create fifo for current_a rtf_create(3,16’sizeof(double)); ” Create fifo for current_b rtf_create(4,16'sizeof(double)); // Create fifo for voltage_a rtf_create(5,16'sizeof(double)); // Create fifo for voltage_b rtf_create(6,16*sizeof(double)); ”Create fifo for var_a rtf_create(7,16‘sizeof(double)); ” Create fifo for var_b rtf_create(8,16‘sizeof(double)); // Create fifo for var_c rtf_create(9,16*sizeof(double)); // Create fifo for var_d rtf_create(10,16*sizeof(double)); // Create fifo for var_e request_RTirq(7, intr_handler); ”Install interrupt handler outb(inb(0x21)&(~0x80),0x21); ”irq7 setup: set the mask and read pending irq outb(0x20,0x20); control=control_default=inb(LPTC); ”Store initial values control=controll0x10; ”Enable irq7 outb(control,LPTC); ”Enable irq7 control=controll0x20; ”Enable input direction on LPT outb(control,LPTC); ”Enable input direction on LPT outb(inb(LPT2C)l0x20,LPTZC); ”Enable input direction on LPT2 control=control&0xF0; outb(control,LPTC); ”Clear control bits for (i=0;i<20000;i++) ”Reset interrupt bit by pulsing I control=controll0x01; ”RD bit outb(control,LPTC); ”RD bit I for (i=0;i<20000;i++) control=control&0xFE; outb(control,LPTC); } control=controll0x02; ”Enable CONVST outb(control,LPTC); ”Enable CONVST control=control&0xFD; ”Disable CONVST outb(control,LPTC); ”Disable CONVST zero_ticks=rt_get_time(); ”Get time in ticks return 0; } 120 void cleanup_module(void) rtf_destroy(1 0); ”Destroy fifo rtf_destroy(Q); ”Destroy fifo rtf_destroy(8); ”Destroy fifo rtf_destroy(7); ”Destroy fifo rtf_destroy(6); ”Destroy fifo rtf_destroy(S); ”Destroy fifo rtf_destroy(4); ”Destroy fifo rtf_destroy(a); ”Destroy fifo rtf_destroy(2); ” Destroy fifo rtf_destroy(1); ”Destroy fifo control=control&(~0x10); ”Disable irq7 outb(control,LPTC); ”Disable irq7 outb(control_default,LPTC); ”Replace initial values free_RTirq(7); ”Uninstall interrupt handler I 121 8-2 OUTPUT DATA PROGRAME FOR ANALYSIS user.c - this program is run by typing "user" will prompt for file name. The output data is used for analysis of on line results. In this thesis Matlab is used for analyses of data. #define NUM_SAMPLES 40016 #define MODULE #define BASE_ADDRESS (127*0x100000) #include #include #include #include #include #include #include #include #include #include #include #include int main(void) I int rt_ int to_user_1,rt_to_user_2,rt_to_user_3,rt_to_user_4,rt_to-user_5; rt_to_user_6,rt_to_user_7,rt_to_user_8,rt_to_user_9,rt_to_user_10; int 1; double double double double double double double double double double stor_seconds[NUM_SAMPLES]; stor_current_a[NUM_SAMPLES]; stor_current_b[NUM_SAMPLES]; stor_voltage_a[NUM_SAMPLES]; stor_voltage_b[NUM_SAMPLES]; stor_var_a[NUM_SAMPLES]; stor_var_b[NUM_SAMPLES]; stor_var_c[NUM_SAMPLES]; stor_var_d[NUM_SAMPLES]; stor_var_e[NUM_SAMPLES]; FILE *fp; char datafile_name[20]; double current_a,current_b,voltage_a,voltage_b,seconds; double var_a,var_b,var_c,var_d,var_e; setpriority(PRIO_PROCESS,0,-20); // Increase priority // Open fifo if ((rt_to_user_l = I fprintf(stderr, open('/dev/rtf1", O_RDONLY)) < 0) "Error opening /dev/rtf1\n'); exit(l); ) 122 // Open fifo if ((rt_to_user_z { fprintf(stderr, exit(1); } // Open fifo if ((rt_to_user_B { fprintf(stderr, exitll); } // Open fifo if ((rt_to_user_4 I fprintf(stderr, exit(1); } // Open fifo if ((rt_to_user_S { fprintf(stderr, exit(1); } // Open fifo if ((rt_to_user_6 { fprintf(stderr, exit(1); } // Open fifo if ((rt_to_user_7 { fprintflstderr, exit(1); } // Open fifo if ((rt_to_user_B I fprintf(stderr, exit(1); } // Open fifo if ((rt_to_user_9 { fprintf(stderr, exit(1); } = open("/dev/rtf2", O_RDONLY)) "Error opening /dev/rtf2\n"); = open('/dev/rtf3", O_RDONLY)) "Error opening /dev/rtf3\n'); = open("/dev/rtf4”, O_RDONLY)) "Error opening /dev/rtf4\n"); open("/dev/rtf5", O_RDONLY)) "Error opening /dev/rtf5\n"); open('/dev/rtf6", O_RDONLY)) "Error opening /dev/rtf6\n“); open('/dev/rtf7", O_RDONLY)) ”Error opening /deV/rtf7\n'); = open("/dev/rtf8", O_RDONLY)) "Error opening /dev/rtf8\n'); = open('/dev/rtf9", O_RDONLY)) "Error opening /dev/rtf9\n"); 123 0) 0) 0) 0) 0) 0) O) 0) // Open fifo if ((rt_to_user_lO = open("/dev/rtf10", O_RDONLY)) < O) I fprintflstderr, "Error opening /dev/rtf10\n'); exit(1); } for (i=0 ; i